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Other types of frequency

Angular frequency ω (in radians per second), is larger than frequency ν (incycles per second, also called Hz), by a factor of 2 π .

Angular frequency ω is defined as the rate of changeof angular displacement (during rotation), or in the phase of a sinusoidal waveform (e.g. in oscillations and waves):

.Angular frequency is measured in radians per second(rad/s).

Spatial frequency is analogous to temporal frequency,but the time axis is replaced by one or more spatialdisplacement axes.Wavenumber is the spatial analogue of angular frequency. In case of more than one spatial dimension,wavenumber is a vector quantity.

Frequency of wavesFrequency has an inverse relationship to the conceptof wavelength ; simply, frequency is inverselyproportional to wavelength λ (lambda ). Thefrequency f is equal to the phase velocity v of the wave divided by the wavelength λ of the wave:

In the special case of electromagnetic waves movingthrough a vacuum , then v = c , where c is the speed of light in a vacuum, and this expression becomes:

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When waves from a monochrome source travel fromone medium to another, their frequency remains exactlythe same — only their wavelength and speed change.

FrequencyFor other uses, see Frequency (disambiguation) .

Three flashing lights, from lowest frequency (top) to highest frequency(bottom). f is the frequency in Hertz ("Hz"), meaning the number of flashes per second. T is the period in seconds ("s"), meaning the number of seconds per

flash. T and f are reciprocals .Frequency is the number of occurrences of a repeating event per unit time . It is also referred to as temporal frequency .The period is the duration of one cycle in a repeating event, sothe period is the reciprocal of the frequency. Loosely speaking,1 year is the period of the Earth 's orbit around the Sun ,[1] andthe Earth's rotation on its axis has a frequency of 1 rotation per day. [2]

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3. Characteristics of SoundA sound can be characterized by the following three quantities:

(i) Pitch.(ii) Quality.(iii) Loudness.Pitch is the frequency of a sound as perceived by human ear. Ahigh frequency gives rise to a high pitch note and a low frequencyproduces a low pitch note. Figure 2 shows the frequencies of samecommon sounds.

Figure 2 Frequency and Wavelength of Everyday Sound A pure tone is the sound of only one frequency, such as that givenby a tuning fork or electronic signal generator.

The fundamental note has the greatest amplitude and is heardpredominantly because it has a larger intensity. The otherfrequencies such as 2f o , 3f o , 4f o , ............. arecalled overtones or harmonics and they determine the quality of the sound.Loudness is a physiological sensation. It depends mainly on soundpressure but also on the spectrum of the harmonics and the physicalduration.

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The frequency of sound is the number of air pressure oscillations per second at a fixedpoint occupied by a sound wave.

The amplitude is the magnitude of sound pressure change within the wave. Basically this isthe maximum amount of pressure at any point in the sound wave. A sound wave is causedliterally by increases in pressure at certain points causing a "domino effect" outward, thehigher pressure points are the crests in a sound wave , and behind them are low pressurepoints which tail them. These are known as the troughs on a wavelength graph. Sound'spropagation Velocity depends largely on the type, temperature and pressure of themedium through which it propagates. Because air is nearly a perfect gas, the speed of sound does not depend on air pressure.

The frequency range of sound that is audible to humans is approx. between 20 and 20,000Hz. This range of course varies between individuals, and goes down as are age increases.Sounds will begin to damage our ears at 85 dBSPL and sounds above approximately 130dBSPL will cause pain, as a result are known as the: "threshold of pain". Of course againthis range will vary among individuals and will change with age.

Sound in brief but remarkeable terms is a vibration, that

our ears percieve by the sense of hearing. Mostcommonly vibrations travel to our ears via the air. Theear then converts these sound waves into nerve impulsesthat are sent to our brains, where the impulses becomesound. To say all that in a more technical language:Sound "is an alternation in pressure, particledisplacement, or particle velocity propagated in an elastic

material" (Olson 1957). Sound is also a series of mechanical compressions and rarefactions or longitudinalwaves that successively propagate through media thatare at least a little compressible. What causes soundwaves is known as "the source of waves". Examples of sounds sources is: A violin string that vibrates uponbeing bowed or plucked.

Frequency of SoundSound is the quickly varying pressure wave travelling through a medium. Whensound travels through air, the atmospheric pressure varies periodically. The numberof pressure variations per second is called the frequency of sound, and is measured in

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Hertz (Hz) which is defined as cycles per second.

The higher the frequency, the more high-pitched a sound is perceived. The soundsproduced by drums have much lower frequencies than those produced by a whistle,as shown in the following diagrams. Please click on the demo button to hear theirsounds and the difference in pitch.

The crest factor or peak-to-average ratio (PAR ) or peak-to-average power ratio (PAPR ) is a measurement of a waveform , calculated from the peak amplitude of the waveformdivided by the RMSvalue of the waveform.

Examples

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DC voltages have a crest factor of 1 since the RMS and the peakamplitude are equal, and it is the same for a squarewave (irrespective of duty cycle ).This table provides values for some other normalized waveforms :

Wave type Waveform

Peak magnitude (rectified)

RMS value

Crestfactor

Crestfactor(dB)

DC 1 1 1 0.0 dB

Sine wave 1[1]

3.01dB

Full-waverectified sine 1

[1]

3.01dB

Half-waverectified sine 1 [1

]

6.02dB

Triangle wave 1 4.77dB

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Square wave 1 1 1 0 dB

PWM -Signal 1[1]

dB

QPSK 3.5–4dB

8VSB 6.5–8.1dB [2]

64QAM 7.7 dB128QAM 8.2 dB

WCDMA downlink carrier

10.6dB

OFDM ~12 dB

RefractionFrom Wikipedia, the free encyclopedia

For the property of metals, see refraction (metallurgy) . For themagic effect, see David Penn (magician) . For the refraction inatmosphere, see Atmospheric refraction .

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An image of the Golden Gate Bridge is refracted and bent by many differingthree dimensional drops of water

Refraction in a Perspex ( acrylic ) block.

Refraction is the change in direction of a wave due to a changein its speed . This is most commonly observed when a wavepasses from one medium to another at any angle other than 90°or 0°. Refraction of light is the most commonly observedphenomenon, but any type of wave can refract when it interactswith a medium, for example when sound waves pass from onemedium into another or when water waves move into water of adifferent depth. Refraction is described by Snell's law , whichstates that the angle of incidence θ 1 is related to the angle of refraction θ 2 by

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where v 1 and v 2 are the wave velocities in the respectivemedia, and n1 and n 2 the refractive indices . In general, theincident wave is partially refracted and partially reflected ; thedetails of this behavior are described by the Fresnelequations .

Contents

[hide ]

• 1 Explanation• 2 Clinical

significance

• 3 Acoustics• 4 See also• 5 References• 6 External links

[edit ]Explanation

Refraction of light waves in water. The dark rectangle represents the

actual position of a pencil sitting in a bowl of water. The light rectanglerepresents the apparent position of the pencil. Notice that the end (X)looks like it is at (Y), a position that is considerably shallower than (X).

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The straw appears to be broken, due to refraction of light as it emergesinto the air.

Refraction of light at the interface between two media of different refractive indices , with n 2 > n 1. Since the phase velocity is lower in the second medium (v 2 < v1), the angle of refraction θ 2 is less than theangle of incidence θ 1; that is, the ray in the higher-index medium is closer to the normal.

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Light on air–plexi surface in this experiment mainly undergoes refraction(lower ray) and to a lesser extent reflection (top ray)

Photograph of refraction of waves in a ripple tank

Diagram of refraction of water waves

In optics , refraction occurs when waves travel from a mediumwith a given refractive index to a medium with another at anangle. At the boundary between the media, the wave's phasevelocity is altered, usually causing a change in direction.

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Its wavelength increases or decreases butits frequency remains constant. For example, a light ray willrefract as it enters and leaves glass , assuming there is achange in refractive index. A ray traveling along the normal(perpendicular to the boundary) will change speed, but notdirection. Refraction still occurs in this case. Understanding of this concept led to the invention of lenses and the refractingtelescope . Refraction can be seen when looking into a bowl of water. Air has a refractive index of about 1.0003, and water has a refractive index of about 1.33. If a person looks at astraight object, such as a pencil or straw, which is placed at aslant, partially in the water, the object appears to bend at the

water's surface. This is due to the bending of light rays as theymove from the water to the air. Once the rays reach the eye,the eye traces them back as straight lines (lines of sight). Thelines of sight (shown as dashed lines) intersect at a higher position than where the actual rays originated. This causes thepencil to appear higher and the water to appear shallower thanit really is. The depth that the water appears to be whenviewed from above is known as the apparent depth . This is animportant consideration for spearfishing from the surfacebecause it will make the target fish appear to be in a differentplace, and the fisher must aim lower to catch the fish.The diagram on the right shows an example of refractionin water waves . Ripples travel from the left and pass over ashallower region inclined at an angle to the wavefront. Thewaves travel more slowly in the shallower water, so thewavelength decreases and the wave bends at the boundary.The dotted line represents the normal to the boundary. The

dashed line represents the original direction of the waves. Thisphenomenon explains why waves on a shoreline tend to strikethe shore close to a perpendicular angle. As the waves travelfrom deep water into shallower water near the shore, they arerefracted from their original direction of travel to an angle morenormal to the shoreline. [1] Refraction is also responsible

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for rainbows and for the splitting of white light into a rainbow-spectrum as it passes through a glass prism . Glass has ahigher refractive index than air. When a beam of white lightpasses from air into a material having an index of refractionthat varies with frequency, a phenomenon knownas dispersion occurs, in which different coloured componentsof the white light are refracted at different angles, i.e., theybend by different amounts at the interface, so that theybecome separated. The different colors correspond to differentfrequencies.While refraction allows for beautiful phenomena such asrainbows, it may also produce peculiar optical phenomena ,

such as mirages and Fata Morgana . These are caused by thechange of the refractive index of air with temperature.Recently some metamaterials have been created which havea negative refractive index . With metamaterials, we can alsoobtain total refraction phenomena when the wave impedancesof the two media are matched. There is then no reflectedwave. [2]

Also, since refraction can make objects appear closer thanthey are, it is responsible for allowing water to magnify objects.First, as light is entering a drop of water, it slows down. If thewater's surface is not flat, then the light will be bent into a newpath. This round shape will bend the light outwards and as itspreads out, the image you see gets larger.A useful analogy in explaining the refraction of light would beto imagine a marching band as they march at an oblique anglefrom pavement (a fast medium) into mud (a slower medium).

The marchers on the side that runs into the mud first will slowdown first. This causes the whole band to pivot slightly towardthe normal (make a smaller angle from the normal).

[edit ]Clinical significance

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In medicine ,particularly optometry , ophthalmology and orthoptics , refraction (also known as refractometry ) is a clinical test in whicha phoropter may be used by the appropriate eye careprofessional to determine the eye's refractive error and thebest corrective lenses to be prescribed. A series of test lensesin graded optical powers or focal lengths are presented todetermine which provide the sharpest, clearest vision. [3]

[edit ]AcousticsIn underwater acoustics , refraction is the bending or curving of a sound ray that results when the ray passes through a sound

speed gradient from a region of one sound speed to a regionof a different speed. The amount of ray bending is dependentupon the amount of difference between sound speeds, that is,the variation in temperature, salinity, and pressure of thewater. [4] Similar acoustics effects are also found in the Earth'satmosphere . The phenomenon of refraction of sound in theatmosphere has been known for centuries; [5] however,beginning in the early 1970s, widespread analysis of this effectcame into vogue through the designing of urban highways and noise barriers to addressthe meteorological effects of bending of sound rays in thelower atmosphere. [6]

[edit ]See also

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cycle

Refraction

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WavelengthFrom Wikipedia, the free encyclopedia

For other uses, see Wavelength (disambiguation) .

Wavelength of a sine wave , λ, can be measured between any two points withthe same phase , such as between crests, or troughs, or corresponding zerocrossings as shown.

In physics , the wavelength of a sinusoidal wave is the spatialperiod of the wave – the distance over which the wave's shaperepeats. [1] It is usually determined by considering the distance

between consecutive corresponding points of the same phase ,such as crests, troughs, or zero crossings, and is a characteristicof both traveling waves and standing waves , as well as other spatial wave patterns. [2][3] Wavelength is commonly designated bythe Greek letter lambda (λ). The concept can also be applied toperiodic waves of non-sinusoidal shape. [1][4] Theterm wavelength is also sometimes applied to modulated waves,and to the sinusoidal envelopes of modulated waves or wavesformed by interference of several sinusoids. [5]

Assuming a sinusoidal wave moving at a fixed wave speed,wavelength is inversely proportional to frequency : waves withhigher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths. [6]

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Examples of wave-like phenomena are sound waves , light,and water waves . A sound wave is a periodic variation inair pressure , while in light and other electromagnetic radiation thestrength of the electric and the magnetic field vary. Water wavesare periodic variations in the height of a body of water. In acrystal lattice vibration , atomic positions vary periodically in bothlattice position and time.Wavelength is a measure of the distance between repetitions of ashape feature such as peaks, valleys, or zero-crossings, not ameasure of how far any given particle moves. For example, inwaves over deep water a particle in the water moves in a circle of the same diameter as the wave height, unrelated to wavelength. [7]

Contents

[hide ]

• 1 Sinusoidal waves○ 1.1 Standing waves○ 1.2 Mathematical

representation○ 1.3 General media

1.3.1 Nonuniform media1.3.2 Crystals

• 2 More general waveforms○ 2.1 Envelope waves○ 2.2 Wave packets

• 3 Interference anddiffraction

○ 3.1 Double-slitinterference

○ 3.2 Single-slit

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diffraction○ 3.3 Diffraction-limited

resolution• 4 Subwavelength• 5 See also• 6 References• 7 External links

[edit ]Sinusoidal wavesIn linear media, any wave pattern can be described in terms of theindependent propagation of sinusoidal components.The wavelength λ of a sinusoidal waveform traveling at constantspeed v is given by: [8]

Refraction: when a plane wave encounters a medium in which it has aslower speed, the wavelength decreases, and the direction adjustsaccordingly.

where v is called the phase speed (magnitude of the phasevelocity) of the wave and f is the wave's frequency.In the case of electromagnetic radiation —such as light—in free space , the phase speed is the speed of light ,

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about 3×10 8 m/s. For sound waves in air, the speed of sound is343 m/s (1238 km/h) (at room temperature and atmosphericpressure ). As an example, the wavelength of a 100 MHzelectromagnetic (radio) wave is about: 3×10 8 m/s divided by100×10 6 Hz = 3 metres.Visible light ranges from deep red , roughly 700 nm, to violet,roughly 400 nm (430–750 THz) (for other examples,see electromagnetic spectrum ). The wavelengths of soundfrequencies audible to the human ear (20 Hz –20 kHz) arebetween approximately 17 m and 17 mm, respectively,assuming a typical speed of sound of about 343 m/s; thewavelengths in audible sound are much longer than those in

visible light.Frequency and wavelength can change independently, butonly when the speed of the wave changes. For example, whenlight enters another medium, its speed and wavelengthchange while its frequency does not; this change of wavelength causes refraction , or a change in propagationdirection of waves that encounter the interface between mediaat an angle.

Sinusoidal standing waves in a box that constrains the end points to benodes will have an integer number of half wavelengths fitting in the box.

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[edit ]Standing waves

A standing wave (black) depicted as the sum of two propagating wavestraveling in opposite directions (red and blue).

A standing wave is an undulatory motion that stays in oneplace. A sinusoidal standing wave includes stationary points of no motion, called nodes , and the wavelength is twice thedistance between nodes. The wavelength, period, and wavevelocity are related as before, if the stationary wave is viewedas the sum of two traveling sinusoidal waves of oppositelydirected velocities. [9]

[edit ]Mathematical representationTraveling sinusoidal waves are often representedmathematically in terms of their velocity v (in the x direction),frequency f and wavelength λ as:

where y is the value of the wave at any position x andtime t , and A is the amplitude of the wave. They are alsocommonly expressed in terms of (radian) wavenumber k (2π times the reciprocal of wavelength) and angular frequency ω (2π times the

frequency) as:

in which wavelength and wavenumber are related tovelocity and frequency as:

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or

Dispersion causes separation of colors when light isrefracted by a prism.

The relationship between ω and λ (or k ) is calleda dispersion relation . This is not generally asimple inverse relation because the wave

velocity itself typically varies with frequency.[10]

Wavelength is decreased in a medium with higher refractive index.

In the second form given above, thephase ( kx − ωt ) is often generalized to ( k•r − ωt ),by replacing the wavenumber k with a wavevector that specifies the direction andwavenumber of a plane wave in 3-space ,parameterized by position vector r . In that case,

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the wavenumber k , the magnitude of k , is still inthe same relationship with wavelength as shownabove, with v being interpreted as scalar speedin the direction of the wave vector. The first form,using reciprocal wavelength in the phase, doesnot generalize as easily to a wave in an arbitrarydirection.Generalizations to sinusoids of other phases,and to complex exponentials, are also common;see plane wave . The typical convention of usingthe cosine phase instead of the sine phase whendescribing a wave is based on the fact that the

cosine is the real part of the complex exponentialin the wave

[edit ]General mediaThe speed of a wave depends upon themedium in which it propagates. In particular,the speed of light in most media is lower than

in vacuum, which means that the samefrequency will correspond to a shorter wavelength in the medium than in vacuum.The wavelength in the medium is

Various local wavelengths on a crest-to-crestbasis in an ocean wave approaching shore. [11]

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where λ 0 is the wavelength in vacuum,and n(λ0) is the refractive index of themedium, which varies with wavelength.This variation, called dispersion , causesdifferent colors of light to be separatedwhen light is refracted by a prism .When wavelengths of electromagneticradiation are quoted, the vacuumwavelength is usually intended unless thewavelength is specifically identified as thewavelength in some other medium. Inacoustics, where a medium is essential

for the waves to exist, the wavelengthvalue is given for a specified medium.

[ edit ] Nonuniform media

A sinusoidal wave in a nonuniform medium, withloss. As the wave slows down, the wavelengthgets shorter and the amplitude increases; after aplace of maximum response, the shortwavelength is associated with a high loss and the

wave dies out.Wavelength can be a useful concept evenif the wave is not periodic in space. For example, in an ocean wave approachingshore, shown in the figure, the incomingwave undulates with a

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varying local wavelength that depends inpart on the depth of the sea floor compared to the wave height. Theanalysis of the wave can be based uponcomparison of the local wavelength withthe local water depth. [11]

Waves that are sinusoidal in time butpropagate through a medium whoseproperties vary with position(an inhomogeneous medium) maypropagate at a velocity that varies withposition, and as a result may not be

sinusoidal in space. The analysisof differential equations of such systemsis often done approximately, usingthe WKB method (also known asthe Liouville–Green method ). The methodintegrates phase through space using alocal wavenumber , which can beinterpreted as indicating a "localwavelength" of the solution as a functionof time and space. [12][13] This method treatsthe system locally as if it were uniformwith the local properties; in particular, thelocal wave velocity associated with afrequency is the only thing needed toestimate the corresponding localwavenumber or wavelength. In addition,the method computes a slowly changing

amplitude to satisfy other constraints of the equations or of the physical system,such as for conservation of energy in thewave.

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[ edit ] Crystals

A wave on a line of atoms can be interpretedaccording to a variety of wavelengths.

Waves in crystalline solids are notcontinuous, because they are composedof vibrations of discrete particles arrangedin a regular lattice. Thisproduces aliasing because the samevibration can be considered to have avariety of different wavelengths, as shownin the figure. [14] Descriptions using more

than one of these wavelengths areredundant; it is conventional to choose thelongest wavelength that fits thephenomenon. The range of wavelengthssufficient to provide a description of allpossible waves in a crystalline mediumcorresponds to the wave vectors confinedto the Brillouin zone .[15]

This indeterminacy in wavelength in solidsis important in the analysis of wavephenomena such as energybands and lattice vibrations . It ismathematically equivalent to

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the aliasing of a signal that is sampled atdiscrete intervals.

[edit ]More general waveformsA wave moving in space is calleda traveling wave . If the shape repeatsitself, it is also a periodic wave .[16] In thespecial case of uniform anddispersionless media (see Dispersionrelation ), at a fixed moment in time, asnapshot of the wave shows a repeatingform in space, with characteristics such as

peaks and troughs repeating at equalintervals. To an observer at a fixedlocation the amplitude appears to vary intime, and repeats itself with acertain period , for example T . If the spatialperiod of this wave is referred to as itswavelength, then during every period, onewavelength of the wave passes theobserver. In dispersion and uniformmedia, the wave propagates withunchanging shape and the velocity in themedium is uniform, so this period impliesthe wavelength is:

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Near-periodic waves over shallow water havesharper crests and flatter troughs than thoseof a sinusoid.

This duality of space and time isexpressed mathematically by the factthat, in such special media, the wave'sbehavior does not dependindependently on position x and time t ,but rather on the combination of position and time x − vt . The wave'samplitude u is then expressedas u ( x − vt ) and in the case of a

periodic function u with period λ , thatis, u ( x + λ − vt ) = u ( x − vt ), theperiodicity of u in space means that asnapshot of the wave at a giventime t finds the wave varyingperiodically in space with period λ . In asimilar fashion, this periodicityof u implies a periodicity in time aswell: u ( x − v(t + T) ) = u ( x − vt ) usingthe relation vT = λ described above, soan observation of the wave at a fixedlocation x finds the wave undulatingperiodically in time with period T = λ /v .[16]

Traveling waves with non-sinusoidalwave shapes can occur inlinear dispersionless media such asfree space, but also may arise innonlinear media under certaincircumstances. For example, large-amplitude ocean waves with certainshapes can propagate unchanged,because of properties of the nonlinear

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surface-wave medium. [17] An exampleis the cnoidal wave , a periodictraveling wave named because it isdescribed by the Jacobian ellipticfunction of m-th order, usually denotedas cn (x; m) .[18]

[edit ]Envelope wavesThe term wavelength is alsosometimes applied to the envelopes of waves, such as the travelingsinusoidal envelope patterns thatresult from the interference of twosinusoidal waves close in frequency;such envelope characterizations areused in illustrating the derivationof group velocity , the speed at whichslow envelope variations propagate. [19]

[edit ]Wave packets

A propagating wave packet; in general,the envelope of the wave packet moves at adifferent speed than the constituent waves. [20]

Main article: Wave packet

Localized wave packets , "bursts" of wave action where each wave packettravels as a unit, find application in

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many fields of physics; the notion of awavelength also may be applied tothese wave packets. [21] The wavepacket has an envelope that describesthe overall amplitude of the wave;within the envelope, the distancebetween adjacent peaks or troughs issometimes called a local wavelength .[22][23] Using Fourier analysis , wavepackets can be analyzed into infinitesums (or integrals) of sinusoidal wavesof different wavenumbers or

wavelengths.[24]

Louis de Broglie postulated that allparticles with a specific valueof momentum have a wavelength

where h is Planck's constant ,and p is the momentum of theparticle. This hypothesis was at thebasis of quantum mechanics .Nowadays, this wavelength iscalled the de Broglie wavelength .For example, the electrons ina CRT display have a De Brogliewavelength of about 10 −13 m. Toprevent the wave function for such

a particle being spread over allspace, De Broglie proposed usingwave packets to represent particlesthat are localized in space. [25] Thespread of wavenumbers of sinusoids that add up to such a

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wave packet corresponds to anuncertainty in the particle'smomentum, one aspect of the Heisenberg uncertaintyprinciple .[24]

[edit ]Interference anddiffraction[edit ]Double-slitinterferenceMain article: Interference (wave

propagation)

Pattern of light intensity on a screen for light passing through two slits. The labelson the right refer to the difference of thepath lengths from the two slits, which areidealized here as point sources.

When sinusoidal waveforms add,they may reinforce each other (constructive interference) or cancel each other (destructiveinterference) depending upon their relative phase. This phenomenonis used in the interferometer . A

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simple example is an experimentdue to Young where light is passedthrough two slits .[26]As shown in thefigure, light is passed through twoslits and shines on a screen. Thepath of the light to a position on thescreen is different for the two slits,and depends upon the angle θ thepath makes with the screen. If wesuppose the screen is far enoughfrom the slits (that is, s is largecompared to the slit separation d )

then the paths are nearly parallel,and the path difference issimply d sin θ. Accordingly thecondition for constructiveinterference is: [27]

where m is an integer, and for destructive interference is:

Thus, if the wavelength of the light is known, the slitseparation can bedetermined from theinterference patternor fringes , and vice versa .

It should be noted that theeffect of interference isto redistribute the light, sothe energy contained in thelight is not altered, justwhere it shows up. [28]

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[edit ]Single-slitdiffractionMain

articles: Diffraction and Diffr action formalism

The notion of path differenceand constructive or destructive interferenceused above for the double-slit experiment applies aswell to the display of a single

slit of light intercepted on ascreen. The main result of this interference is to spreadout the light from the narrowslit into a broader image onthe screen. This distributionof wave energy iscalled diffraction .

Two types of diffraction aredistinguished, dependingupon the separationbetween the source and thescreen: Fraunhofer diffraction or far-fielddiffraction at largeseparations and Fresneldiffraction or near-fielddiffraction at closeseparations.In the analysis of the singleslit, the non-zero width of the slit is taken into account,

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and each point in theaperture is taken as thesource of one contribution tothe beam of light ( Huygen'swavelets ). On the screen,the light arriving from eachposition within the slit has adifferent path length, albeitpossibly a very smalldifference. Consequently,interference occurs.In the Fraunhofer diffraction

pattern sufficiently far from asingle slit, within a small-angle approximation , theintensity spread S is relatedto position x via asquared sinc function :[29]

with where L is the slitwidth, R is the distanceof the pattern (on thescreen) from the slit, andλ is the wavelength of light used. Thefunction S has zeroswhere u is a non-zerointeger, where areat x values at aseparation proportion towavelength.

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[edit ]Diffraction-limited resolutionMain articles: Angular

resolution and Diffraction-limited system

Diffraction is thefundamental limitation onthe resolving power of optical instruments, suchas telescopes (includingradiotelescopes )

and microscopes .[30]

For a circular aperture, thediffraction-limited imagespot is known as an Airydisk ; the distance x in thesingle-slit diffractionformula is replaced byradial distance r and thesine is replaced by 2 J 1,where J 1 is a firstorder Bessel function .[31]

Theresolvable spatial size of objects viewed through amicroscope is limitedaccording tothe Rayleigh criterion ,the radius to the first nullof the Airy disk, to a sizeproportional to thewavelength of the lightused, and depending onthe numerical aperture :[32]

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where the numerical

aperture is definedas for θbeing the half-angleof the cone of raysaccepted bythe microscopeobjective .The angular size of

the central brightportion (radius to firstnull of the Airy disk)of the imagediffracted by acircular aperture, ameasure mostcommonly used for telescopes andcameras, is: [33]

where λ is thewavelength of thewaves that arefocused for

imaging, D the entrancepupil diameter of the imagingsystem, in thesame units, and

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the angular resolution δ is inradians.As with other diffractionpatterns, thepattern scales inproportion towavelength, soshorter wavelengths canlead to higher

resolution.[edit ]SubwavelengthTheterm subwaveleng th is used todescribe an objecthaving one or more dimensionssmaller than thelength of the wavewith which theobject interacts.For example, theterm subwaveleng

th-diameter optical fibre meansan opticalfibre whosediameter is less

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than thewavelength of light propagatingthrough it.A subwavelengthparticle is aparticle smaller than thewavelength of light with which itinteracts(see Rayleigh

scattering ).Subwavelength apertures are holessmaller than thewavelength of light propagatingthrough them.Such structureshave applicationsin extraordinaryopticaltransmission ,and zero-modewaveguides ,among other areasof photonics .

Subwavelength may also refer to aphenomenoninvolvingsubwavelengthobjects; for

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example, subwavelength imaging .

Audio compression is a form of data compression designed toreduce the transmission bandwidth requirement of digital audiostreams and the storage size of audio files . Audiocompression algorithms are implemented in computer software as audio codecs . Generic data compression algorithmsperform poorly with audio data, seldom reducing data size muchbelow 87% from the original, [citation needed ] and are not designed for use in real time applications. Consequently, specifically optimizedaudio lossless and lossy algorithms have been created. Lossyalgorithms provide greater compression rates and are used in

mainstream consumer audio devices.In both lossy and lossless compression, informationredundancy is reduced, using methods such as coding , patternrecognition and linear prediction to reduce the amount of information used to represent the uncompressed data.The trade-off between slightly reduced audio quality andtransmission or storage size is outweighed by the latter for mostpractical audio applications in which users may not perceive theloss in playback rendition quality. For example, one CompactDisc holds approximately one hour of uncompressed high fidelitymusic, less than 2 hours of music compressed losslessly, or 7hours of music compressed in the MP3 format at medium bitrates .

REFLECTION OF SOUND

After reading this section you will be able to do the following:• Observe the experiment below and explain why the wave reacts

differently depending on what surface it hits.

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• Discuss how echoes are made.

The Multi-Material Room

Questions

1. What happens when a sound wave hits a concave shaped surface?

2. Is the sound reflected back to the source from a concave shapedsurface more or less than that reflected from a flat surface?

3. What happens when a sound wave hits the porous surface?4. What happens when a sound wave hits an irregular surface?

Reflection

When sound reflects off a special curved surface called a parabola , it willbounce out in a straight line no matter where it originally hits. Manystages are designed as parabolas so the sound will go directly into theaudience, instead of bouncing around on stage. If the parabola is closed

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off by another curved surface, it is called an ellipse . Sound will travelfrom one focus to the other, no matter where it strikes the wall. Awhispering gallery is designed as an ellipse. If your friend stands at onefocus and you stand at the other, his whisper will be heard clearly by you.No one in the rest of the room will hear anything.Reflection is responsible for many interesting phenomena. Echoes are thesound of your own voice reflecting back to your ears. The sound you hearringing in an auditorium after the band has stopped playing is caused byreflection off the walls and other objects. A sound wave will continue tobounce around a room, or reverberate, until it has lost all its energy. Awave has some of its energy absorbed by the objects it hits. The rest islost as heat energy.

Sound Absorption

Everything, even air, absorbs sound. One example of air absorbing soundwaves happens during a thunderstorm. When you are very close to astorm, you hear thunder as a sharp crack. When the storm is fartheraway, you hear a low rumble instead. This is because air absorbs highfrequencies more easily than low. By the time the thunder has reached

you, all the high pitches are lost and only the low ones can be heard. The

best absorptive material is full of holes that sound waves can bouncearound in and lose energy. The energy lost as heat is too small to be felt,though, it can be detected by scientific instruments.

How does sound reach every point in the room?

Since sound travels in a straight path from its source, how does it getaround corners? You already know that if you and your friend are standingon either side of a wall and there is an open door nearby, you will be ableto hear what your friend says. Because you would not hear your friend ifthe door was closed, sound is not traveling through the wall. Instead, itmust be going around the corner and out the door.

You hear your friend because of sound diffraction. Diffraction uses theedges of a barrier as a secondary sound source that sends waves in a newdirection. These secondary waves overlap and interfere with each other

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and the original waves, making the sound less clear. Working together,diffraction and reflection can send sounds to every part of a room.Acoustic absorption is that property of any material thatchanges the acoustic energy of sound waves into another form,often heat , which it to some extent retains, as opposed to thatsound energy that that material reflects or conducts. Acousticabsorption is represented by the symbol A in calculations.Absorption is not a single mechanism of sound attenuation :propagation through a heterogeneous system is affectedby scattering as well.The absorptivity of a given material is frequency-dependent and isaffected by size, shape, location and the mounting method used.Porous insulative materials such as mineral wool , glass wool areeffective sound absorbers compared with good conductors suchas metals. Micro perforated plates , however, supply "hard"absorptive surfaces.Acoustic absorption is important in the analysis of sonar . Theprimary substance in seawater that is responsible for absorptionis magnesium sulfate . The secondary substance is boric acid . Themost common sea salt, sodium chloride has virtually no effect onsound absorption.

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A laser-acoustic method for testingand classifying hard surface layers

D. Schneider a , , , B. Schultrich a , H.-J. Scheibe a , H. Ziegele a andM. Griepentrog b

a Fraunhofer-Institute for Material and Beam Technology,Winterbergstrasse 28, D-01277 Dresden, Germanyb Bundesanstalt für Materialforschung und -prüfung, Unter den Eichen87, D-12205 Berlin, Germany

Available online 21 September 1999.

AbstractThe laser-acoustic method is accepted to be an interesting method of testing thin films. It is based on measuring the dispersion of surfaceacoustic waves which are generated by short laser pulses. A reliabletest equipment was developed that allows a user-friendly operation.The method is non-destructive, the test takes little time and specialsample preparation is not required. It is mainly applied to measure theYoung’s modulus of thin films with thickness down to less than 50 nm.

Recent studies showed these results to correlate with importantmicrostructural and mechanical properties of hard and superhardfilms. The laser-acoustic technique was improved to test multilayer films consisting of two components. The approach of an effectivemedium of transversal symmetry is used to describe the elastic

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behavior of multilayer films. It enables the elastic anisotropy of themultilayer film to be evaluated. Applications are presented, performedat multilayers of diamond-like carbon and aluminum deposited by

laser-arc on steel and silicon. The films consisted of four and twentysingle layers, respectively. The Young’s modulus of the diamond-likecarbon in the multilayer was determined with the laser-acoustictechnique. The results reveal the reproducibility of the depositiontechnique and demonstrate the potential of the laser-acoustictechnique to test multilayer films. The laser-acoustic method is shownto be sensitive to machining layers. The effect of grinding and

polishing steel surfaces was studied. Studies were performed tocompare the results of the laser-acoustic technique with those of membrane deflection and micro-indentation. TiN, CrN and TiCN films(thickness: 0.8–2.3 μm) were tested with laser-acoustics and micro-indentation, polysilicon films (thickness: 0.46 μm) with laser-acousticsand the membrane deflection technique.

Keywords: Young's modulus; Multilayer films; Diamond-like carbon;Titanium nitrate; Surface acoustic waves; Micro-indentation

Optimization of zinc oxide thin filmfor surface acoustic wave filters byradio frequency sputtering

Y. Yoshino , a , b , T. Makino b , Y. Katayama b and T. Hata a

a Graduate School of Natural Science and Technology, KanazawaUniversity, Kanazawa, Ishikawa 920-8667, Japan

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b R&D division, Murata Mfg. Co., Ltd., Yasu, Shiga 520-2393, Japan

Available online 25 September 2000.

AbstractElectrical characteristics of zinc oxide (ZnO)/glass surface acousticwave (SAW) filters, the structure of which is ZnO thin film on a glasssubstrate with aluminum inter digital transducers, are greatlyinfluenced by deposition parameters of a radio frequency sputtering

for making ZnO thin films. The deposition conditions for making theZnO thin film are also considered to obtain good piezoelectricity for SAW devices. Oxygen concentration in the radio frequency sputteringgreatly affects the properties of ZnO thin films. The interfacemicrostructure of ZnO thin films is investigated by cross-sectiontransmission electron spectroscopy. The growth figures of ZnO onglass and ZnO on Al are similar. The average crystal size of ZnO onglass is larger than that of ZnO on Al.

Common Expressions: anechoicExpressions Definition

Anechoic chamber A chamber having very little reverberation. Source: Wordnet 3.0 Copyright ©2006 by Princeton University. All rights reserved.

Anechoic chamber An anechoic chamber is a room that is isolated from externalsound or electromagnetic radiation sources, sometimes usingsound proofing, and prevents the reflection of wave phenomena

(reverberation). Anechoic chambers are widely used for measuring the acoustic properties of acoustic instruments,measuring the transfer functions of electro-acoustic devices,testing microphones and performing psychoacousticsexperiments (such as measuring the quality of audio codecs or measuring head-related transfer functions). (references )

Anechoic room An anechoic room simulates a free field — a representation of atheoretical infinite space, in which there are no sound wave

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reflections (echoes). In rooms such as these, the only soundswhich exist are emitted directly from their source, and notreflected from another part of the chamber. Anechoic rooms havethe characteristic of being muted, muffled, and silent. (references )

Anechoic tiles Anechoic tiles are rubber or sorbathane like tiles containing

thousands of tiny voids, applied to the outer hulls of militaryships and submarines.

Specialty Expressions: anechoicExpressions Domain Definition

Anechoicchamber

Business A sound cavity in a horn or siren that minimizes echoes andvibrations. (references )

Dead Room , 2000architectural sound installation360 x 360 x 240cm(h), variable

Stills from video

- - -

> video clip <

the death instinct is now only puresilence in its transcendent distinctionfrom life, but it infuses all the more,

throughout all the immanent combination it forms with this same

life.G. Deleuze and F. Guattari Anti-

Oedipus: Capitalism and Schizophrenia

The exterior, is covered with soundinsulation cones baring the aesthetics of a dark grey science fiction fortress.These walls are precursors to the surrealhypnotic atmosphere of the interior asthey themselves gently pulse in a bio-mechanical rhythm.One can often find a visitor walkingslowly around the cube, dragging a handagainst its tactile surface, lost in asensual revolution around the structure.

Somewhere in between the aesthetics of a car interior and an insane asylum cell,and bearing a glowing sterilityreminiscent of a coffin or hospital, theinstallation's interior is a bright whitevinyl padded cell. For 3 minutes and 33seconds at a time, eight large sub-woofers pulse a rhythm of bassfrequencies that are too low for thehuman ear to actually hear,interweaving amongst its references theaverage radio play duration of thetypical pop song as well as Cagiantrajectories of 'silence'.The space is silent, but the sound canbe seen as the woofers throb their playcycles, felt as the sound waves movethrough the body creating a subtleintangible disturbance, and heard in the'helium voice' disruption of the visitors'voices. Visitors experience a subtly, yetever present re-perception of the body.

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live roomDefinition

noun

• in a recording studio , a large room in which a band can play their

instruments together and be recorded

Refrigeration is a process in which work is done to move heatfrom one location to another. Refrigeration has many applications

including but not limited to; household refrigerators, industrialfreezers, cryogenics, air conditioning, and heat pumps. In order tosatisfy the Second Law of Thermodynamics , some form of workmust be performed to accomplish this. The work is traditionallydone by mechanical work but can also be doneby magnetism , laser or other means.

Methods of refrigerationMethods of refrigeration can be classified as non-cyclic , cyclic and thermoelectric .

[edit ]Non-cyclic refrigerationIn non-cyclic refrigeration, cooling is accomplished bymelting ice or by subliming dry ice (frozen carbon dioxide). Thesemethods are used for small-scale refrigeration such as inlaboratories and workshops, or in portable coolers .Ice owes its effectiveness as a cooling agent to itsconstant melting point of 0 °C (32 °F). In order to melt, ice mustabsorb 333.55 kJ/kg (approx. 144 Btu/lb) of heat. Foodstuffsmaintained at this temperature or slightly above have anincreased storage life.

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Solid carbon dioxide has no liquid phase at normal atmosphericpressure, so sublimes directly from the solid to vapor phase at atemperature of -78.5 °C (-109.3 °F), and is therefore effective for maintaining products at low temperatures during the period of sublimation. Systems such as this where the refrigerantevaporates and is vented into the atmosphere are known as "totalloss refrigeration".

[edit ]Cyclic refrigerationMain article: Heat pump and refrigeration cycle

This consists of a refrigeration cycle, where heat is removed froma low-temperature space or source and rejected to a high-temperature sink with the help of external work, and its inverse,the thermodynamic power cycle . In the power cycle, heat issupplied from a high-temperature source to the engine, part of theheat being used to produce work and the rest being rejected to alow-temperature sink. This satisfies the second law of thermodynamics .A refrigeration cycle describes the changes that take place in therefrigerant as it alternately absorbs and rejects heat as itcirculates through a refrigerator . It is also applied to HVACR work,when describing the "process" of refrigerant flow through anHVACR unit, whether it is a packaged or split system.Heat naturally flows from hot to cold. Work is applied to cool aliving space or storage volume by pumping heat from a lower temperature heat source into a higher temperature heatsink. Insulation is used to reduce the work and energy required toachieve and maintain a lower temperature in the cooled space.

The operating principle of the refrigeration cycle was describedmathematically by Sadi Carnot in 1824 as a heat engine .The most common types of refrigeration systems use the reverse-Rankine vapor-compression refrigeration cyclealthough absorption heat pumps are used in a minority of applications.

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Cyclic refrigeration can be classified as:1. Vapor cycle, and2. Gas cycle

Vapor cycle refrigeration can further be classified as:1. Vapor-compression refrigeration2. Vapor-absorption refrigeration

[ edit ] Vapor-compression cycle(See Heat pump and refrigeration cycle and Vapor-compression refrigeration for more details)

The vapor-compression cycle is used in most household

refrigerators as well as in many large commercial andindustrial refrigeration systems. Figure 1 provides a schematicdiagram of the components of a typical vapor-compressionrefrigeration system.

Figure 1: Vapor compression refrigeration

The thermodynamics of the cycle can be analyzed on adiagram [11][12] as shown in Figure 2. In this cycle, a circulatingrefrigerant such as Freon enters the compressor as a vapor.From point 1 to point 2, the vapor is compressed atconstant entropy and exits the compressor as a vapor at a

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higher temperature, but still below the vapor pressure at thattemperature. From point 2 to point 3 and on to point 4, thevapor travels through the condenser which cools the vapor until it starts condensing, and then condenses the vapor into aliquid by removing additional heat at constant pressure andtemperature. Between points 4 and 5, the liquid refrigerantgoes through the expansion valve (also called a throttle valve)where its pressure abruptly decreases, causing flashevaporation and auto-refrigeration of, typically, less than half of the liquid.

Figure 2: Temperature–Entropy diagram

That results in a mixture of liquid and vapor at a lower temperature and pressure as shown at point 5. The cold liquid-vapor mixture then travels through the evaporator coil or tubes

and is completely vaporized by cooling the warm air (from thespace being refrigerated) being blown by a fan across theevaporator coil or tubes. The resulting refrigerant vapor returns to the compressor inlet at point 1 to complete thethermodynamic cycle.

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The above discussion is based on the ideal vapor-compression refrigeration cycle, and does not take intoaccount real-world effects like frictional pressure drop in thesystem, slight thermodynamic irreversibility during thecompression of the refrigerant vapor, or non-idealgas behavior (if any).More information about the design and performance of vapor-compression refrigeration systems is available in theclassic Perry's Chemical Engineers' Handbook .[13]

[ edit ] Vapor absorption cycleMain article: Absorption refrigerator

In the early years of the twentieth century, the vapor absorption cycle using water-ammonia systems was popular and widely used. After the development of the vapor compression cycle, the vapor absorption cycle lost much of itsimportance because of its low coefficient of performance (about one fifth of that of the vapor compressioncycle). Today, the vapor absorption cycle is used mainlywhere fuel for heating is available but electricity is not, such asin recreational vehicles that carry LP gas . It is also used inindustrial environments where plentiful waste heat overcomesits inefficiency.The absorption cycle is similar to the compression cycle,except for the method of raising the pressure of the refrigerantvapor. In the absorption system, the compressor is replacedby an absorber which dissolves the refrigerant in a suitableliquid, a liquid pump which raises the pressure and a

generator which, on heat addition, drives off the refrigerantvapor from the high-pressure liquid. Some work is required bythe liquid pump but, for a given quantity of refrigerant, it ismuch smaller than needed by the compressor in the vapor compression cycle. In an absorption refrigerator, a suitablecombination of refrigerant and absorbent is used. The most

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common combinations are ammonia (refrigerant) and water (absorbent), and water (refrigerant) and lithiumbromide[absorbent].

[ edit ] Gas cycleWhen the working fluid is a gas that is compressed andexpanded but doesn't change phase, the refrigeration cycle iscalled a gas cycle . Air is most often this working fluid. As thereis no condensation and evaporation intended in a gas cycle,components corresponding to the condenser and evaporator in a vapor compression cycle are the hot and cold gas-to-gas heat exchangers in gas cycles.

The gas cycle is less efficient than the vapor compressioncycle because the gas cycle works on the reverse Braytoncycle instead of the reverse Rankine cycle . As such theworking fluid does not receive and reject heat at constanttemperature. In the gas cycle, the refrigeration effect is equalto the product of the specific heat of the gas and the rise intemperature of the gas in the low temperature side. Therefore,for the same cooling load, a gas refrigeration cycle will requirea large mass flow rate and would be bulky.Because of their lower efficiency and larger bulk, air cycle coolers are not often used nowadays in terrestrialcooling devices. The air cycle machine is very common,however, on gas turbine -powered jet aircraft becausecompressed air is readily available from the engines'compressor sections. These jet aircraft's cooling andventilation units also serve the purpose of pressurizing theaircraft.

Echo

In musicIn music performance and recording, electric echo effects havebeen used since the 1950s. The Echoplex is a tape delay effect ,

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first made in 1959 that recreates the sound of an acoustic echo.Designed by Mike Battle, the Echoplex set a standard for theeffect in the 1960s and was used by most of the notable guitar players of the era; original Echoplexes are highly soughtafter.While Echoplexes were used heavily by guitar players (andthe occasional bass player, such as Chuck Rainey , or trumpeter,such as Don Ellis ), many recording studios also used theEchoplex.Beginning in the 1970s, Market built the solid-state Echoplex for Maestro. In the 2000s, most echo effectsunits use electronic or digital circuitry to recreate the echo effect.

Acoustic phenomenon

If so many reflections arrive at a listener that they are unable todistinguish between them, the proper term is reverberation . Anecho can be explained as a wave that has been reflected by adiscontinuity in the propagation medium , and returns withsufficient magnitude and delay to be perceived. Echoes arereflected off walls or hard surfaces like mountains and privacyfences.

This illustration depicts the principle of sediment echo sounding, which uses anarrow beam of high energy and low frequency

When dealing with audible frequencies, the human ear cannotdistinguish an echo from the original sound if the delay is lessthan 1/10 of a second. Thus, since the velocity of sound is

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approximately 343 m/s at a normal room temperature of about20°C, the reflecting object must be more than 17.15 m from thesound source at this temperature for an echo to be heard by aperson at the source.Sound travels approximately 343 meters/s (1100 ft/s). If a soundproduces an echo in 2 seconds, the object producing the echowould be half that distance away (the sound takes half the time toget to the object and half the time to return). The distance for anobject with a 2-second echo return would be 1 sec X 343 meters/sor 343 meters (1100 ft). In most situations with human hearing,echoes are about one-half second or about half this distance,since sounds grow fainter with distance. In nature, canyon walls

or rock cliffs facing water are the most common natural settingsfor hearing echoes.The strength of an echo is frequentlymeasured in dB sound pressure level SPL relative to the directlytransmitted wave. Echoes may be desirable (as in sonar ) or undesirable (as in telephone systems).

Acoustic Sound DiffusionPosted on July 4, 2010 by Albro

Sound diffusion reduces the problems with firstreflections and because the diffusive materials havean irregular surface, flutter echo is eliminated.However, reverberation will not be eliminated, butthe scattering or breaking up of the reflections tendsto result in a smoother reverberation at a lowerlevel.Sound diffusion materials can be pricey, and

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the devices are difficult to build, however, a regular bookcase loaded with books of different sizes will

break up the sound wave reflections and redirect the waves in various ways. Sound Diffusion controlsreflections by breaking up an audio wave intosmaller waves that are scattered in many differentdirections. This method also controls echo and

reverb at lower frequencies.

Another method for sound diffusion is the use of quadratic diffusers. The idea is to arrange wells, or

blocks and strips of wood, or other materials in an

array, each at a different depth. The more wells, blocks and strips of wood installed in a given area,the better the high-frequency sound diffusion; thedeeper the wells or variations in blocks or strips, the

better the low-frequency performance. AuralexSpaceArray diffusers (retailing at about $798.00)combine hemispherical acoustical diffusion with atop quality wood finish. Besides the beauty of thispaulownia wood, the craftsmanship is exceptional

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and the musical qualities provided by this diffusercan give a room sound quality that isn’t quantifiable.

Strong yet lightweight, the beautiful 24″x24″ solid wood panels are easy to install and can be used in a variety of placement options.For audio professionals who seek to provide a smallroom acoustical environment supportive of a wide

range of performance and recording styles,the Aurelex pArtScience™ SpaceCoupler (retails atabout $500.00 ea) is an acoustical treatment thatcreates a natural “large sound” within a small roomarea. Unlike current alternatives, which involve

custom design and remodeling, the SpaceCoupler works within the current room footprint for afraction of the cost.New applications for the SpaceCoupler are beingdiscovered daily. Coupled together, like the AurelexSCREEN6 Kit (retails at about $1200), thisconfiguration of Space Couplers increase absorberefficiency and its high-end appearance all make the

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Aurelex Screen6 Kit an exciting product for sounddiffusion.

Other solutions for sound diffusion are engineeredinto the design during the construction phase of astudio; nonrectangular rooms, wall splaying, andcurved or angled ceilings. The term nonrectangularrooms refers to the process of making sure you do

not have parallel walls. Wall splaying refers to theprocess of bumping out a parallel wall in onedirection, either from the top or bottom, or left toright. Ceiling treatments, such as curving or angling,need to be considered during the design and

engineering process as they require special framingand finishes.

And then there are other practical commercialelements available for the audio, recording andarchitectural industries. These diffusers are designedusing mathematical equations to solve the reflectionproblems. These types of sound reflection solutions

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can be purchased from companies that specialize indiffusion products.

Sound CoolingAcousticians Use Sound Waves to RefrigerateFood

April 1, 2004

To chill Ben & Jerry's ice cream, a new freezer employssound waves and harmless gases in place of the moving

parts and hazardous chemicals in traditional refrigerators.The "thermoacoustic freezer" is very efficient, cheap and environmentally friendly.

How can sound waves chill objects?

Conventional refrigerators chill items by

compressing and expanding chemicalscalled refrigerants. This transfers heatfrom inside the fridge to the outside, cooling the inside.Sound waves can do the same job: very powerful soundwaves can also conduct heat. In an acoustic refrigerator,helium is compressed in a small steel cylinder to a pressure10 times that of the Earth's atmosphere. Then a speaker

blasts a long unchanging note, sending sound wavesvibrating through the helium-filled cylinder.

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The pressure changes caused by the sound waves bouncing

around in the sealed space alternately heat and cool theenclosed gas.

The sound waves force the helium through a fine-meshedstainless steel screen, and heat is transferred from the gas tothe steel. As the sound passes through the screens, it causes

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the sound wave to drop in pressure. This causes the heliumto expand and cool even more before it reaches a reservoirof ethyl alcohol.

The now-cold helium draws heat from the alcohol. The coldalcohol is then pumped through the walls of the refrigeratorto cool the inside, and pumped back to the reservoir, wherethe helium chills it again.

Your ear works much like the acoustic refrigerator. Soundwaves inside your ear vibrate the eardrum. As the eardrumswings back and forth, a fluid inside picks up those waves,

just like the refrigerator's helium cylinder. Instead of turningthe energy from the waves into heat, as the refrigeratordoes, the waves' energy vibrates tiny hairs that are tuned tothe different pitches of the sound. The sound you hearconsists of different frequencies or wavelengths, whichdetermine their pitch.

Loud sounds can cause pain at 120 dB -- what you wouldhear near the stage at a heavy metal concern. At 165 dB,your hair would catch fire from the heat caused by thefriction from the sound vibrations. Acoustic refrigerators havesound levels of 173-196 dB -- similar to the sound of a spaceshuttle launch at ground zero -- safely contained in apressurized tube. Even if the tube shattered, the sound

would instantly spread out through the atmosphere andreturn to harmless levels.A1 temative Fluorocarbons Environmental 'Acceptability StudyRefrigeration and Air Conditioning Technology WorkshopBreckenridge Hilton, Breckenridge, CO

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June 23-25,1993THERMOACOUSTIC REFRIGERATIONSteven L. Garrett, Thomas J. Hofler, and David K. Perkins

Physics Department and Space Systems Academic GroupNaval Postgraduate School, Monterey, CA 939431 .O TECHNOLOGY DESCRIPTIONI . I Historical Perspective. The thermoacoustic heat pumpingcycle is the youngest technologythat will be presented at this workshop. Although the reverseprocess - the generation of sound by

an imposed temperature gradient - had been observed for severalcenturies by glassblowersl~l andfor decades by cryogenic researchersP1; the recognition thatuseful amounts of heat could bepumped against a substantial temperature gradient with acoefficient-of-performance which is asignificant fraction of the Camot limit was only made ten years

agoU1, with the first demonstration,including efficiency measurements, being made in 1986141.This discovery was made even more significant by therecognition that the thermoacousticheat pumping cycle was intrinsically irreversible. Traditional heatengine cycles, such as theCamot Cycle typically studied in elementary thermodynamics

courses, assume that the individualsteps in the cycle are reversible. In thermoacoustic engines, theirreversibility due to the imperfect(diffusive) thermal contact between the acoustically oscillatingworking fluid and a stationary

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second thermodynamic medium (the "stack") provides therequired phasing. This "naturalphasing"[41 has produced heat engines which require nomoving parts other than the self-maintained oscillations of the working fluid.During this relatively short period, several refrigerators andprime movers have beenfabricated and tested at Los Alamos National Laboratories[3-5]and two refrigerators for spacecraftapplications were built at the Naval Postgraduate School. TheSpace ThermoAcousticRefrigeratorL'I was flown on the Space Shuttle Discovery (STS-42) in January, 1992, and theThermoAcoustic Life Sciences Refrigerator (TALSR)[81 is nowbeing tested and should becharacterized completely by October, 1993.- 1 - S. L. Garrett, et. al. ThermoAcoustic Refrigeration AFEASWorkshopTALSR was designed to pump 700 Btuhr in the refrigerator mode(+4"C) and 400 Btu/hr inthe freezer mode (-2273. This makes it the first thermoacousticrefrigerator which would becapable of operation as a conventional domestic foodrefngeratodfreezer. At the present time, thereare several preliminary designs which should be capable of one-

half ton to three tons of air conditioning capacity, but no prototypes are currently under construction.1.2 A Simple Invisid Model of the Thermoacoustic HeatPumping Process. Although a

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complete and detailed analysis of the thermoacoustic heatpumping process is well beyond thescope of this paper, the following simple, invisid, Lagrangianrepresentation of the cycle containsthe essence of the process. A complete analysis[6] wouldnecessarily include the gas viscosity,finite wavelength effects, longitudinal thermal conduction alongthe stationary secondthermodynamic medium and through the gas, and the ratio of the gas and solid dynamic heatcapacities.A schematic diagram of a simple, one-quarter wavelengththermoacoustic refrigerator isshown in Figure 1.*Rigid.:Termination 1Loudspeaker

TubeI, IFigure 1. Schematic diagram of a one-quarter wavelengththermoacoustic refrigerator.I IThe thermal penetration depth, 6,, represents the distance over which heat will diffuse duringa time which is on the order of an acoustic period, T = l/f, where f is the acoustic frequency. It isdefined[9] in terms of the thermal conductivity of the gas, K, thegas density, p, and its isobaric

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specific heat (per unit mass), cp.This length scale is crucial to understanding the performance of the thermoacoustic cycle since the

diffusive heat transport between the gas and the "stack" is onlysignificant within this region. It isfor that reason that the stack and the spacing between its platesare central to the thermoacousticcycle.-2- S. L. Garrett, et. al. ThermoAcoustic Refrigeration A FEASWorks hop

For this analysis we will focus our attention on a small portionof a single plate surfacefrom the solid stack material is small enough that a substantialamount of thermal conduction cantake place in an amount of time which is on the order of theacoustic period. In the lower half of Figure 1, a small portion of the stack has been magnified and aparcel of gas undergoing anacoustic oscillation is shown. The four steps in the cycle arerepresented by the four boxes whichare shown as moving in a rectangular path for clarity. In realitythey simply oscillate back andforth. As the fluid oscillates back and forth along the plate, itundergoes changes in temperaturedue to the adiabatic compression and expansion resulting from

the pressure variations whichaccompany the standing sound wave. The compressions andexpansions of the gas whichconstitute the sound wave are adiabatic if they occur far from thesurface of the plate. The relation

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between the change in gas pressure due to the sound wave, p1,relative to the mean (ambient)pressure, pm, and the adiabatic temperature change of the gas,TI, due to the acoustic pressurechange, relative to the mean absolute (Kelvin) temperature, T,, isgiven below in equation (2).8within the "stack" and the adjacent gas which is undergoingacoustic oscillations. The distanceAlthough the oscillations in an acoustic heat pump are sinusoidalfunctions of time, Figure 1depicts the motion as articulated (a square wave) in order tosimplify the explanation. The plate isassumed to have a mean temperature, T,, and a temperaturegradient,VT, referenced to the meanposition, x = 0. The temperature of the plate at the left-mostposition of the gas parcels excursionis therefore T, - xlVT, and at the right-most excursion is T, +xlVT.In the first step of this four-step cycle, the fluid is transportedalong the plate by a distance2x1 and is heated by adiabatic compression from a temperatureof T, - x1VT to Tm - xlVT -+ 2Tl.The adiabatic gas law provides the relationship between thechange in gas pressure, p1, and the

associated change in temperature, T,, as described in equation(2). Because we are considering aheat pump, work, in the form of sound, was done on the gasparcel hence it is now a temperaturewhich is higher than that of the plate at its present location (ix.,IxlVTI < ITlI).

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In the second step, the warmer gas parcel transfers an amount of heat, dQhob to the plate bythermal conduction at constant pressure and its temperaturedecreases to that of the plate, Tm +xlVT. In the third step, the fluid is transported back along theplate to position -XI and is cooledby adiabatic expansion to a temperature T, + xlVT - 2T1. Thistemperature is lower than theoriginal temperature at location -XI, so in the fourth step the gasparcel adsorbs an amount of heat,dQcold, from the plate thereby raising its temperature back to itsoriginal value, Tm - xlVT.- 3 - S. L. Garrett, et. al. ThermoAcoustic Refrigeration AFEASWorkshopThe net effect of this process is that the system has completed acycle which has returned it toits original state and an amount of heat, dGold, has beentransported PD a temDerature mdient by

work done in the form of sound. It should be stressed again thatno mechanical devices were usedto provide the proper phasing between the mechanical motionand the thermal effects.If we now consider the full length of the stack as shown in theupper portion of Figure 1, theoverall heat pumping process is analogous to a "bucket brigade"

in which each set of gas parcelspicks up heat from its neighbor to the left at a lower temperatureand hands off the heat to itsneighbor to the right at a higher temperature. Heat exchangersare placed at the ends of the stack to

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absorb the useful heat load at the left-hand (cold) end of the stackand exhaust the heat plus work(enthalpy) at the right-hand (hot) end of the stack. The fact thatthe gas parcels actudy move adistance which has typically been on the order of severalmillimeters means that intimate physicalcontact between the heat exchangers and the stack is not crucial.2.0 APPLICATIONSThe applications of thermoacoustic engines fall into twocategories which depend upon

whether the refrigerator is powered by electricity or by heat.Although the heat driventhermoacoustic refrigerators and cryocoolers are attractive for applications where there is abundantheat or waste heat, at the present time, only twothermoacoustically driven refrigerators have beendemonstrated. The first was a "beer cooler"[5JOl and the secondwas a thermoacoustically drivenorifice-pulse-tube cryocooler designated the "Coolahoop"[lll. Amore compact commercialversion of the Coolahoop is now under development for cooling of high speed electronics. Severalother heat-driven thermoacoustic refrigerators are currently in thedesign stages for the aboveapplications including a refrigerator for storage of medical

supplies and vaccines in Bangladesh, asolar driven refrigerated cargo container for transportation of tropical fruits, and a natural gasliquefaction plant.

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Work on electrically powered thermoacoustic refrigeration has,until last year, beenconcentrated on laboratory experiments and spacecraftapplications. At the present time, FordMotor Company is developing thermoacoustic refrigerators for proprietary applications. NPS iscurrently developing two refrigerators. One is a third-generation,single-stage thermoacousticcryocooler (TAR-3) which is designed to reach high-T,superconductor transition temperatures.The other is TALSR, which is capable of producing coolingcomparable to commercial domesticrefrigerator/freezers. TALSR was also designed for use on-boardthe Space ShuttleI81. The firstcommercial application of a TALSR-like design, which will use aless expensive driver, will betargeted to a %iche" market which we are unwilling to disclose atthis time.

Due to the simplicity of its operation and the use of only onemoving part, thermoacousticrefrigeration is also be suitable for cooling the latest generation of computer chips which can run attwice their room temperature design speeds when their temperature is reduced to -50°C.-4- S. L. Garrett, et. al. ThermoAcoustic Refrigeration AFEAS

Workshopi/

Figure 2. Cross-sectional diagram of the half-wavelengthresonant TALSR. Two separate

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drivers are used for redundancy in space applications. Acommercial unit would use a singledouble-acting drive. The two stacks and four fluid-filled heatexchangers are configured so that thetotal temperature span is greater than that of either individualstack.3.0 BENEFITS3.1 Inert working fluid. Helium, being an inert gas, cannotparticipate in chemical re actionsand hence no toxicity, flammability, or negative environmentaleffects (ODP=GWP=O).3.2 No sliding seals or lubrication. Due to the high frequencyoperation, high powers can beachieved with small displacements so no sliding seals or gasbearings are required. This alsomeans that no "tight tolerance" machined parts are requiredthereby reducing manufacturing costs.3.3 Veryfew simple components. Electrically driven systemsrequire only one moving part andthermally driven systems have no moving parts. The "stack" canbe fabricated from cheap plastics.3.4 Large range of working temperatures. Depending upon theposition and length of the stackin the acoustic standing wave field, one can trade off thetemperature span and the heat pumping

power. Different working fluids are therefore not required for different temperature ranges.3.5 Intrinsically suited to proportional control. Just as one is ableto control the volume of astereo system, a electrically driven thermoacoustic refrigerator'scooling power is continuously

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variable. This allows improved overall efficiency by doing rapidcool-down at a lower COP andthen maintaining heat leak losses at higher COP. This "loadmatching" can also reduce heatexchanger inefficiencies by minimizing temperature differenceswithin the fluids and exchangers.3.6 Immaturity. Thennoacoustics is the youngest of the heatengine cycles. It is more likelythat important breakthroughs which substantially improveperformance and manufacturability willstill occur here rather than the older technologies which havealready "skimmed the cream".- 5 - S. L. Garrett, et. al. ThermoAcoustic Refrigeration A F EASWorkshop4.0 TECHNICAL ISSUES4.1 immaturity. Because thermoacoustics is the youngest of existing heat engine cycles, it lacksthe infrastructure (suppliers, sales and service base, educationalprograms, etc.) which can enhancemarketability. In addition, since there are presently nocommercial products on the market,thermoacoustics does not have a "cash flow" which can be"tapped" to make either incrementalcomponent improvements or to finance general research anddevelopment efforts.

4.2 Eficiency. Although computer models[121 of TALSR predictthat it will have a Coefficient-of-Performance Relative to Carnot (COPR) of 42% (exclusiveof motor inefficiencies andsecondary heat exchange fluid pumps), TALSR has not yetbeen tested. The previous

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thermoacoustic cryocooler designs have been optimized for temperature span rather than COP.Their best measured performance has given a COPR I20%,again exclusive of electroacousticefficiency.4.3 Power density. The simple boundary layer models of thermoacoustic engineperformance[d121 may not apply as acoustical amplitudes areincreased. If acoustic mach numbersare restricted to Ma&%, then the realizable power density of conventional thermoacoustic stackgeometries may be restricted to 10 Tons (35 kW) per squaremeter of stack cross-sectional area atworking fluid pressures below 20 atm. Higher power researchrefrigerators and numericalhydrodynamic computer simulations would be very useful todetermine what would ultimately limitthe power density.4.4 Electroacoustic conversion. Although electrical to acousticalconversion efficiencies on theorder of 90% are, in principle, realizable at reasonable cost,present thermoacoustic drivers havehad electroacoustic efficiencies under 50%. This should not be aproblem since efficiencies for similar linear motor technology in Stirling applications as high as

93% have been measured[W.4.5 Secondary heat transfer. All thermoacoustic enginesproduced thus far have used either conduction for small heat loads (<IO Watts) or electrically pumpedheat exchange fluids for large

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heat loads (>IO0 Watts). Unlike the vapor compression (Rankine)cycles, the working fluid in athermoacoustic refrigerator/chiller is not circulated outside theengine. In order to obtain maximumoverall efficiency (Le., net COP), it is therefore necessary tosimultaneously optimize primary andsecondary heat exchanger geometry, transfer fluidthermophysical parameters, transfer fluid flowrates, and electrical pump or heat pipe performance, all subject toeconomic constraints, in order toachieve the best performance at the lowest cost.4.6 The "talent bottleneck." Because thermoacoustics is a newscience and requires expertise ina diverse number of non-traditional disciplines within therefrigeration and HVAC communities(acoustics, transduction, gas mixture thermophysics, PID, PLLand AGC control, etc.), there arevery few experimentalists who are interested or capable of research in this field. This severelylimits the number of potentially promising applications which canbe pursued simultaneously.-6- S. L. Garrett, et. al. ThermoAcoustic Refrigeration AFEASWorkshop5.0 ECONOMICSAll thermoacoustic engines which have been produced to date

have been research prototypes.The costs have been typically 1-2 M$, which accounts primarilyfor scientific and technical staff salaries. No systematic cost projections or comparisons toexisting system costs have been

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attempted. Limited commercialization attempts which addressniche applications are expected over the next three years and should begin to provide some economicbenchmarks which would lead toreliable cost estimates.6.0 TECHNOLOGY OUTLOOKThose of us who work with thermoacoustics feel the outlook isbright for the reasonsenumerated in Section 3.0 of this paper. We recognize that our strongly positive outlook is both

prejudicial and self-serving. On the other hand, the failure of technology outlook projections madeby those who are not knowledgeable in thermoacoustics can beequally prejudicial, self-serving,and more importantly, wrong. This may be best illustrated bythe recent analysis of "EnergyEfficient Alternatives to Chlorofluorocarbons" prepared for theDepartment of Energy by A. D.Little, Inc. In that study[141, several domestic refrigerationtechnologies were ranked from 1(Lowest) to 5 (Highest) based on the probability of success andassigned a 1-5 priority for R&Dsupport.In that A. D. Little analysis, Stirling Cycle was evaluated in theareas of analytical tools,

linear drive systems, compact heat exchangers, reliability, andmarket potential of prototypedesigns. The sum of the scores for "probability of success" and"R&D priority" averaged 8.4 f

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0.6 out of a possible maximum sum of 10. The sum for thermoacoustics (improperly labeledThermal Acoustic) was 2, with the minimum sum being 2! Of theother fourteen technologiesevaluated in that table, none of the others had a sum lower thanfive.The ultimate failure of that A. D. Little analysis can best beestablished by the "head-to-head"comparison that was sponsored by the Life Sciences Division of NASA. In an attempt to replacethe existing Space Shuttle Life Sciences refrigerator/freezer,NASA awarded three contracts tocompanies with potential replacement technologies. One wentto A. D. Little for a scrollpumphapor compression technology. The other two contractswent to Sunpower, Inc., for alinear motor Stirling technology and to NPS for thermoacoustics. As of the date of this

conference, less than a year after the award of the NPS contract,the A. D. Little team has droppedout and the Stirling system has been delivered with only one-thirdof the originally specified heatpumping capability. At this point, it appears that only thethermoacoustic technology will meet theoriginal contract specifications.

When attempting to predict the future utility of a new discovery or emerging technology, it isalways useful to recall the observations made by Prof. Faraday,D.C.L., F.R.S., in 1817[151:- 7 - S. L. Garrett, et. al. ThermoAcoustic Refrigeration AFEASWorkshop

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AbsorptionOne solution to reflections is to apply absorption to the wall, whichturns acoustic energy into heat - this is a kind of damping . Thisabsorption can be a specialist product such as those made of mineral wool, open cell foam, or recycled fibrous material likepaper-waste, but absorption can also be provided by morecommonplace object such as curtains, sofas or carpets. It can bea tricky balance for an acoustic designer - too much absorption,and the room will sound 'dead'. The sound quality would be likelistening outdoors, where only the direct sound from a source isheard (assuming 'soft' ground and an absence of nearbybuildings). While a few people favour such acoustic 'non-environments' for mixing music, for most people these are rather oppressive spaces too far removed from normal listeningconditions.So - what other tricks can the acoustic desgner use?

DiffusionAcoustic Diffusers are used to disperse reflections spatially - to'spread out' reflected sound energy over a wide range of angles -as shown in the diagram above. Some diffusion can be obtainedby carefully placing book cases and other furniture in a room, but

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often specialist (=expensive!) diffusing surfaces can achievegreater diffusion in a more controlled manner. By using sounddiffusers, first order reflections are dispersed to be heard later bythe listener, and by removing and delaying early reflections,diffusion and absorption can make a small music studio soundlike a larger room. Consequently, design is all about locating thereflection points for first order reflections, and applyingappropriate treatment there.Diffusion , in acoustics and architectural engineering , is theefficacy by which sound energy is spread evenly in a givenenvironment. A perfectly diffusive sound space is one that hascertain key acoustic properties which are the same anywhere in

the space. A non-diffuse sound space would have considerablydifferent reverberation time as the listener moved around theroom. Virtually all spaces are non-diffuse. Spaces which arehighly non-diffuse are ones where the acoustic absorption isunevenly distributed around the space, or where two differentacoustic volumes are coupled. The diffusiveness of a sound fieldcan be measured by taking reverberation time measurements at alarge number of points in the room, then taking the standarddeviation on these decay times. Alternately, the spatial distributionof the sound can be examined. Small sound spaces generallyhave very poor diffusion characteristics at low frequencies due toroom modes.

Refraction of Sound

Refraction is the bending of waves when they enter a medium where their speed isdifferent. Refraction is not so important a phenomenon with sound as it is with lightwhere it is responsible for image formation by lenses , the eye , cameras , etc.

But bending of sound waves does occur and is an interesting phenomena in sound

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Diffraction of Sound

Diffraction: the bending of waves around small* obstacles andthe spreading out of waves beyond small* openings.

* small compared to the wavelength

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Sound Focusing and Sound DistributionDiagrams of an auditorium with sound focusing and sound distribution