sounds of music study guide

8/12/2019 Sounds of Music Study Guide

1/56

Sounds of music study guide

Sound is amechanical wavethat results from the back and forth vibration of theparticles of the medium through which the sound wave is moving. If a sound wave ismoving from left to right through air, then particles of air will be displaced both

rightward and leftward as the energy of the sound wave passes through it. The motionof the particles is parallel (and anti-parallel) to the direction of the energy transport.This is what characterizes sound waves in air aslongitudinal waves.

A vibrating tuning fork is capable of creating such a longitudinal wave. As the tines of

the fork vibrate back and forth, they push on neighboring air particles. The forward

motion of a tine pushes air molecules horizontally to the right and the backward

retraction of the tine creates a low-pressure area allowing the air particles to move back

to the left.

Because of the longitudinal motion of the air particles, there are regions in the air

where the air particles are compressed together and other regions where the air

particles are spread apart. These regions are known

as compressionsand rarefactionsrespectively. The compressions are regions of high

air pressure while the rarefactions are regions of low air pressure. The diagram below

depicts a sound wave created by a tuning fork and propagated through the air in an

open tube. The compressions and rarefactions are labeled.

The wavelengthof a wave is merely the distance that a disturbance travels along the

medium in one complete wave cycle. Since a wave repeats its pattern once every wave

cycle, the wavelength is sometimes referred to as the length of the repeating patterns -

the length of one complete wave. For a transverse wave, this length is commonly

measured from one wave crest to the next adjacent wave crest or from one wave

trough to the next adjacent wave trough. Since a longitudinal wave does not contain

crests and troughs, its wavelength must be measured differently. A longitudinal wave

consists of a repeating pattern of compressions and rarefactions. Thus, the wavelength

is commonly measured as the distance from one compression to the next adjacent

compression or the distance from one rarefaction to the next adjacent rarefaction.
http://www.physicsclassroom.com/Class/sound/u11l1a.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1a.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1a.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1b.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1b.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1b.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1b.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1a.cfm


2/56

Since a sound wave consists of a repeating pattern of high-pressure and low-pressure

regions moving through a medium, it is sometimes referred to as a pressure wave. If

a detector, whether it is the human ear or a man-made instrument, were used to detect

a sound wave, it would detect fluctuations in pressure as the sound wave impinges

upon the detecting device. At one instant in time, the detector would detect a high

pressure; this would correspond to the arrival of a compression at the detector site. At

the next instant in time, the detector might detect normal pressure. And then finally a

low pressure would be detected, corresponding to the arrival of a rarefaction at the

detector site. The fluctuations in pressure as detected by the detector occur at periodic

and regular time intervals. In fact, a plot of pressure versus time would appear as a

sine curve. The peak points of the sine curve correspond to compressions; the low

points correspond to rarefactions; and the "zero points" correspond to the pressure that

the air would have if there were no disturbance moving through it. The diagram below

depicts the correspondence between the longitudinal nature of a sound wave in air and

the pressure-time fluctuations that it creates at a fixed detector location.

The above diagram can be somewhat misleading if you are not careful. The

representation of sound by a sine wave is merely an attempt to illustrate the sinusoidal

nature of the pressure-time fluctuations. Do not conclude that sound is a transverse

wave that has crests and troughs. Sound waves traveling through air are indeed

longitudinal waves with compressions and rarefactions. As sound passes through air (or

any fluid medium), the particles of air do not vibrate in a transverse manner. Do not be

misled - sound waves traveling through air are longitudinal waves.

Atransverse waveis a wave in which the particles of the medium are displaced in a

direction perpendicular to the direction of energy transport. A transverse wave can be

created in a rope if the rope is stretched out horizontally and the end is vibrated back-

and-forth in a vertical direction. If a snapshot of such a transverse wave could be taken

so as to freezethe shape of the rope in time, then it would look like the following

diagram.
http://www.physicsclassroom.com/Class/waves/u10l1c.cfm#transversehttp://www.physicsclassroom.com/Class/waves/u10l1c.cfm#transversehttp://www.physicsclassroom.com/Class/waves/u10l1c.cfm#transversehttp://www.physicsclassroom.com/Class/waves/u10l1c.cfm#transverse


3/56

The dashed line drawn through the center of the diagram represents theequilibrium or

rest positionof the string. This is the position that the string would assume if there

were no disturbance moving through it. Once a disturbance is introduced into the string,

the particles of the string begin to vibrate upwards and downwards. At any given

moment in time, a particle on the medium could be above or below the rest position.

Points A, E and H on the diagram represent the crests of this wave. The crestof a

wave is the point on the medium that exhibits the maximum amount of positive or

upward displacement from the rest position. Points C and J on the diagram represent

the troughs of this wave. Thetroughof a wave is the point on the medium thatexhibits the maximum amount of negative or downward displacement from the rest

position.

The wave shown above can be described by a variety of properties. One such property

is amplitude. The amplitudeof a wave refers to the maximum amount of displacement

of a particle on the medium from its rest position. In a sense, the amplitude is the

distancefrom rest to crest. Similarly, the amplitude can be measured from the rest

position to the trough position. In the diagram above, the amplitude could be measured

as the distance of a line segment that is perpendicular to the rest position and extends

vertically upward from the rest position to point A.

The wavelength is another property of a wave that is portrayed in the diagram above.

The wavelengthof a wave is simply the length of one complete wave cycle. If you

were to trace your finger across the wave in the diagram above, you would notice that

your finger repeats its path. A wave is a repeating pattern. It repeats itself in a periodic

and regular fashion over both time and space. And the length of one such spatial

repetition (known as a wave cycle) is the wavelength. The wavelength can be

measured as the distance from crest to crest or from trough to trough. In fact, the

wavelength of a wave can be measured as the distance from a point on a wave to the

corresponding point on the next cycle of the wave. In the diagram above, the

wavelength is the horizontal distance from A to E, or the horizontal distance from B to F,or the horizontal distance from D to G, or the horizontal distance from E to H. Any one

of these distance measurements would suffice in determining the wavelength of this

wave.
http://www.physicsclassroom.com/Class/waves/u10l1b.cfm#resthttp://www.physicsclassroom.com/Class/waves/u10l1b.cfm#resthttp://www.physicsclassroom.com/Class/waves/u10l1b.cfm#resthttp://www.physicsclassroom.com/Class/waves/u10l1b.cfm#resthttp://www.physicsclassroom.com/Class/waves/u10l1b.cfm#resthttp://www.physicsclassroom.com/Class/waves/u10l1b.cfm#rest


4/56

Alongitudinal waveis a wave in which the particles of the medium are displaced in a

direction parallel to the direction of energy transport. A longitudinal wave can be

created in a slinky if the slinky is stretched out horizontally and the end coil is vibrated

back-and-forth in a horizontal direction. If a snapshot of such a longitudinal wave could

be taken so as to freezethe shape of the slinky in time, then it would look like the

following diagram.

Because the coils of the slinky are vibrating longitudinally, there are regions where they

become pressed together and other regions where they are spread apart. A region

where the coils are pressed together in a small amount of space is known as acompression. Acompressionis a point on a medium through which a longitudinal

wave is traveling that has the maximum density. A region where the coils are spread

apart, thus maximizing the distance between coils, is known as a rarefaction.

A rarefactionis a point on a medium through which a longitudinal wave is traveling

that has the minimum density. Points A, C and E on the diagram above represent

compressions and points B, D, and F represent rarefactions. While a transverse wave

has an alternating pattern of crests and troughs, a longitudinal wave has an alternating

pattern of compressions and rarefactions.

As discussed above, thewavelengthof a wave is the length of one complete cycle of a

wave. For a transverse wave, the wavelength is determined by measuring from crest to

crest. A longitudinal wave does not have crest; so how can its wavelength be

determined? The wavelength can always be determined by measuring the distance

between any two corresponding points on adjacent waves. In the case of a longitudinal

wave, a wavelength measurement is made by measuring the distance from a

compression to the next compression or from a rarefaction to the next rarefaction. On

the diagram above, the distance from point A to point C or from point B to point D

would be representative of the wavelength.

A sound wave, like any other wave, is introduced into a medium by a vibrating object.

The vibrating object is the source of the disturbance that moves through the medium.

The vibrating object that creates the disturbance could be the

vocal cords of a person, the vibrating string and sound board of

a guitar or violin, the vibrating tines of a tuning fork, or the

vibrating diaphragm of a radio speaker. Regardless of what

vibrating object is creating the sound wave, the particles of the medium through which

the sound moves is vibrating in a back and forth motion at a given frequency.
http://www.physicsclassroom.com/Class/waves/u10l1c.cfm#longhttp://www.physicsclassroom.com/Class/waves/u10l1c.cfm#longhttp://www.physicsclassroom.com/Class/waves/u10l1c.cfm#longhttp://www.physicsclassroom.com/Class/waves/u10l2a.cfm#wavelengthhttp://www.physicsclassroom.com/Class/waves/u10l2a.cfm#wavelengthhttp://www.physicsclassroom.com/Class/waves/u10l2a.cfm#wavelengthhttp://www.physicsclassroom.com/Class/waves/u10l2a.cfm#wavelengthhttp://www.physicsclassroom.com/Class/waves/u10l1c.cfm#long


5/56

Thefrequency of a waverefers to how often the particles of the medium vibrate when a

wave passes through the medium. The frequency of a wave is measured as the number

of complete back-and-forth vibrations of a particle of the medium per unit of time. If a

particle of air undergoes 1000longitudinal vibrationsin 2 seconds, then the frequency

of the wave would be 500 vibrations per second. A commonly used unit for frequency is

the Hertz (abbreviated Hz), where

1 Hertz = 1 vibration/second

As a sound wave moves through a medium, each particle of the medium vibrates at the

same frequency. This is sensible since each particle vibrates due to the motion of its

nearest neighbor. The first particle of the medium begins vibrating, at say 500 Hz, and

begins to set the second particle into vibrational motion at the same frequency of 500

Hz. The second particle begins vibrating at 500 Hz and thus sets the third particle of the

medium into vibrational motion at 500 Hz. The process continues throughout the

medium; each particle vibrates at the same frequency. And of course the frequency at

which each particle vibrates is the same as the frequency of the original source of thesound wave. Subsequently, a guitar string vibrating at 500 Hz will set the air particles in

the room vibrating at the same frequency of 500 Hz, which carries a sound signalto the

ear of a listener, which is detected as a 500 Hz sound wave.

The back-and-forth vibrational motion of the particles of the medium would not be the

only observable phenomenon occurring at a given frequency. Since a sound wave is

apressure wave,a detector could be used to detect oscillations in pressure from a high

pressure to a low pressure and back to a high pressure. As the compressions (high

pressure) and rarefactions (low pressure) move through the medium, they would reach

the detector at a given frequency. For example, a compression would reach thedetector 500 times per second if the frequency of the wave were 500 Hz. Similarly, a

rarefaction would reach the detector 500 times per second if the frequency of the wave

were 500 Hz. The frequency of a sound wave not only refers to the number of back-

and-forth vibrations of the particles per unit of time, but also refers to the number of

compressions or rarefactions that pass a given point per unit of time. A detector could

be used to detect the frequency of these pressure oscillations over a given period of

time. The typical output provided by such a detector is a pressure-time plot as shown

below.
http://www.physicsclassroom.com/Class/waves/u10l2b.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2b.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1b.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1b.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1b.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1b.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2b.cfm


6/56

Since a pressure-time plot shows the fluctuations in pressure over time, theperiodof

the sound wave can be found by measuring the time between successive high pressure

points (corresponding to the compressions) or the time between successive low

pressure points (corresponding to the rarefactions).As discussed in an earlier unit,the

frequency is simply the reciprocal of the period. For this reason, a sound wave with a

high frequency would correspond to a pressure time plot with a small period - that is, a

plot corresponding to a small amount of time between successive high pressure points.

Conversely, a sound wave with a low frequency would correspond to a pressure time

plot with a large period - that is, a plot corresponding to a large amount of time

between successive high pressure points. The diagram below shows two pressure-time

plots, one corresponding to a high frequency and the other to a low frequency.

The ears of a human (and other animals) are sensitive detectors capable of detecting

the fluctuations in air pressure that impinge upon the eardrum. The mechanics of the

ear's detection ability will be discussedlater in this lesson.For now, it is sufficient to say

that the human ear is capable of detecting sound waves with a wide range of

frequencies, ranging between approximately 20 Hz to 20 000 Hz. Any sound with a

frequency below the audible range of hearing (i.e., less than 20 Hz) is known as

an infrasoundand any sound with a frequency above the audible range of hearing

(i.e., more than 20 000 Hz) is known as an ultrasound. Humans are not alone in their

ability to detect a wide range of frequencies. Dogs can detect frequencies as low as

approximately 50 Hz and as high as 45 000 Hz. Cats can detect frequencies as low as

approximately 45 Hz and as high as 85 000 Hz. Bats, being nocturnal creature, must

rely on sound echolocation for navigation and hunting. Bats can detect frequencies ashigh as 120 000 Hz. Dolphins can detect frequencies as high as 200 000 Hz. While dogs,

cats, bats, and dolphins have an unusual ability to detect ultrasound, an elephant

possesses the unusual ability to detect infrasound, having an audible range from

approximately 5 Hz to approximately 10 000 Hz.

The sensation of a frequency is commonly referred to as the pitchof a sound. A high

pitch sound corresponds to a high frequency sound wave and a low pitch sound
http://www.physicsclassroom.com/Class/waves/u10l2b.cfm#periodhttp://www.physicsclassroom.com/Class/waves/u10l2b.cfm#periodhttp://www.physicsclassroom.com/Class/waves/u10l2b.cfm#periodhttp://www.physicsclassroom.com/Class/waves/u10l2b.cfm#fTrelnhttp://www.physicsclassroom.com/Class/waves/u10l2b.cfm#fTrelnhttp://www.physicsclassroom.com/Class/waves/u10l2b.cfm#fTrelnhttp://www.physicsclassroom.com/Class/sound/u11l2d.cfmhttp://www.physicsclassroom.com/Class/sound/u11l2d.cfmhttp://www.physicsclassroom.com/Class/sound/u11l2d.cfmhttp://www.physicsclassroom.com/Class/sound/u11l2d.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2b.cfm#fTrelnhttp://www.physicsclassroom.com/Class/waves/u10l2b.cfm#period


7/56

corresponds to a low frequency sound wave. Amazingly, many people, especially those

who have been musically trained, are capable of detecting a difference in frequency

between two separate sounds that is as little as 2 Hz. When two sounds with a

frequency difference of greater than 7 Hz are played simultaneously, most people are

capable of detecting the presence of a complex wave pattern resulting from

theinterferenceandsuperpositionof the two sound waves. Certain sound waves when

played (and heard) simultaneously will produce a particularly pleasant sensation when

heard, are said to beconsonant. Such sound waves form the basis of intervalsin

music. For example, any two sounds whose frequencies make a 2:1 ratio are said to be

separated by an octaveand result in a particularly pleasing sensation when heard. That

is, two sound waves sound good when played together if one sound has twice the

frequency of the other. Similarly two sounds with a frequency ratio of 5:4 are said to be

separated by an interval of a third; such sound waves also sound good when played

together. Examples of other sound wave intervals and their respective frequency ratios

are listed in the table below.Interval Frequency Ratio ExamplesOctave 2:1 512 Hz and 256 Hz

Third 5:4 320 Hz and 256 HzFourth 4:3 342 Hz and 256 Hz

Fifth 3:2 384 Hz and 256 Hz

The ability of humans to perceive pitch is associated with the frequency of the sound

wave that impinges upon the ear. Because sound waves traveling through air are

longitudinal waves that produce high- and low-pressure disturbances of the particles of

the air at a given frequency, the ear has an ability to detect such frequencies and

associate them with the pitch of the sound. But pitch is not the only property of a

sound wave detectable by the human ear.

Sound waves are introduced into a medium by the vibration of an object. For example,

a vibrating guitar string forces surrounding air molecules to be compressed and

expanded, creating a pressure disturbance consisting

of an alternating pattern ofcompressions and

rarefactions.The disturbance then travels from particle

to particle through the medium, transporting energy as

it moves. The energy that is carried by the disturbancewas originally imparted to the medium by the vibrating

string. The amount of energy that is transferred to the

medium is dependent upon the amplitude of vibrations

of the guitar string. If more energy is put into the plucking of the string (that is,

moreworkis done to displace the string a greater amount from its rest position), then

the string vibrates with a greater amplitude. The greater amplitude of vibration of the
http://www.physicsclassroom.com/Class/waves/u10l3c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l3c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l3c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l3c.cfm#superposnhttp://www.physicsclassroom.com/Class/waves/u10l3c.cfm#superposnhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/energy/u5l1a.cfmhttp://www.physicsclassroom.com/Class/energy/u5l1a.cfmhttp://www.physicsclassroom.com/Class/energy/u5l1a.cfmhttp://www.physicsclassroom.com/Class/energy/u5l1a.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l3c.cfm#superposnhttp://www.physicsclassroom.com/Class/waves/u10l3c.cfm


8/56

guitar string thus imparts more energy to the medium, causing air particles to be

displaced a greater distance from their rest position. Subsequently, the amplitude of

vibration of the particles of the medium is increased, corresponding to an increased

amount of energy being carried by the particles. Thisrelationship between energy and

amplitudewas discussed in more detail in a previous unit.

Sound Intensity and Distance

The amount of energy that is transported past a given area of the medium per unit of

time is known as the intensityof the sound wave. The greater the amplitude of

vibrations of the particles of the medium, the greater the rate at which energy is

transported through it, and the more intense that the sound wave is. Intensity is the

energy/time/area; and since the energy/time ratio is equivalent to the quantitypower,

intensity is simply the power/area.

Typical units for expressing the intensity of a sound wave are Watts/meter 2.

As a sound wave carries its energy through a two-dimensional or three-dimensional

medium, the intensity of the sound wave decreases with increasing distance from the

source. The decrease in intensity with increasing distance is

explained by the fact that the wave is spreading out over a

circular (2 dimensions) or spherical (3 dimensions) surface and

thus the energy of the sound wave is being distributed over a

greater surface area. The diagram at the right shows that thesound wave in a 2-dimensional medium is spreading out in space

over a circular pattern. Since energy is conserved and the area

through which this energy is transported is increasing, the power

(being a quantity that is measured on a per areabasis) must

decrease.

The mathematical relationship between intensity and distance is sometimes referred to

as an inverse square relationship. The intensity varies inversely with the square of

the distance from the source. So if the distance from the source is doubled (increased

by a factor of 2), then the intensity is quartered (decreased by a factor of 4). Similarly,

if the distance from the source is quadrupled, then the intensity is decreased by a factor

of 16. Applied to the diagram at the right, the intensity at point B is one-fourth the

intensity as point A and the intensity at point C is one-sixteenth the intensity at point A.

Since the intensity-distance relationship is an inverse relationship, an increase in one

quantity corresponds to a decrease in the other quantity. And since the intensity-

distance relationship is an inverse square relationship, whatever factor by which the
http://www.physicsclassroom.com/Class/waves/u10l2c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2c.cfmhttp://www.physicsclassroom.com/Class/energy/u5l1e.cfmhttp://www.physicsclassroom.com/Class/energy/u5l1e.cfmhttp://www.physicsclassroom.com/Class/energy/u5l1e.cfmhttp://www.physicsclassroom.com/Class/energy/u5l1e.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2c.cfm


9/56

distance is increased, the intensity is decreased by a factor equal to the square of

the distance change factor. The sample data in the table below illustrate the inverse

square relationship between power and distance.

Distance Intensity1 m 160 units

2 m 40 units3 m 17.8 units

4 m 10 units

The Threshold of Hearing and the Decibel Scale

Humans are equipped with very sensitive ears capable of detecting sound waves of

extremely low intensity. The faintest sound that the typical human ear can detect hasan intensity of 1*10-12W/m2. This intensity corresponds to a pressure wave in which a

compression of the particles of the medium increases the air pressure in that

compressional region by a mere 0.3 billionth of an atmosphere. A sound with an

intensity of 1*10-12W/m2corresponds to a sound that will displace particles of air by a

mere one-billionth of a centimeter. The human ear can detect such a sound. WOW!

This faintest sound that a human ear can detect is known as the threshold of hearing.

The most intense sound that the ear can safely detect without suffering any physical

damage is more than one billion times more intense than the threshold of hearing.

Since the range of intensities that the human ear can detect is so large, the scale that is

frequently used by physicists to measure intensity is a scale based on powers of 10.

This type of scale is sometimes referred to as a logarithmic scale. The scale for

measuring intensity is the decibel scale. The threshold of hearing is assigned a sound

level of 0 decibels (abbreviated 0 dB); this sound corresponds to an intensity of 1*10 -

12W/m2. A sound that is 10 times more intense ( 1*10 -11W/m2) is assigned a sound level

of 10 dB. A sound that is 10*10 or 100 times more intense (1*10-10W/m2) is assigned a

sound level of 20 db. A sound that is 10*10*10 or 1000 times more intense (1*10-

9W/m2) is assigned a sound level of 30 db. A sound that is 10*10*10*10 or 10000

times more intense (1*10-8W/m2) is assigned a sound level of 40 db. Observe that this

scale is based on powers of 10. If one sound is 10x

times more intense than anothersound, then it has a sound level that is 10*x more decibels than the less intense sound.

The table below lists some common sounds with an estimate of their intensity and

decibel level.

Source Intensity Intensity Level# of Times

Greater Than TOHThreshold of Hearing (TOH) 1*10-12W/m2 0 dB 100


10/56

Rustling Leaves 1*10-11W/m2 10 dB 101

Whisper 1*10-10W/m2 20 dB 102

Normal Conversation 1*10-6W/m2 60 dB 106Busy Street Traffic 1*10-5W/m2 70 dB 107

Vacuum Cleaner 1*10-4W/m2 80 dB 108

Large Orchestra 6.3*10-3

W/m2

98 dB 109.8

Walkman at Maximum Level 1*10-2W/m2 100 dB 1010Front Rows of Rock Concert 1*10-1W/m2 110 dB 1011

Threshold of Pain 1*101W/m2 130 dB 1013

Military Jet Takeoff 1*102W/m2 140 dB 1014Instant Perforation of Eardrum 1*104W/m2 160 dB 1016

A sound wave is apressure disturbancethat travels through a medium by means of

particle-to-particle interaction. As one particle becomes disturbed, it exerts a force on

the next adjacent particle, thus disturbing that particle from rest and transporting the

energy through the medium. Like any wave, thespeed of asound waverefers to how fast the disturbance is passed from

particle to particle. Whilefrequencyrefers to the number of

vibrations that an individual particle makes per unit of time,

speed refers to the distance that the disturbance travels per unit of time. Always be

cautious to distinguish between the two often-confused quantities of speed (how fast...)

and frequency (how often...).

Since the speed of a wave is defined as the distance that a point on a wave (such as a

compression or a rarefaction) travels per unit of time, it is often expressed in units of

meters/second (abbreviated m/s). In equation form, this is

speed = distance/time

The faster a sound wave travels, the more distance it will cover in the same period of

time. If a sound wave were observed to travel a distance of 700 meters in 2 seconds,

then the speed of the wave would be 350 m/s. A slower wave would cover less distance

- perhaps 660 meters - in the same time period of 2 seconds and thus have a speed of

330 m/s. Faster waves cover more distance in the same period of time.

Factors Affecting Wave Speed

The speed of any wavedepends upon the properties of the mediumthrough which the

wave is traveling. Typically there are two essential types of properties that effect wave

speed - inertial properties and elastic properties. Elastic propertiesare those

properties related to the tendency of a material to maintain its shape and not deform

whenever a force or stress is applied to it. A material such as steel will experience a
http://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2d.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2d.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2d.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2d.cfmhttp://www.physicsclassroom.com/Class/sound/u11l2a.cfmhttp://www.physicsclassroom.com/Class/sound/u11l2a.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#mediahttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#mediahttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#mediahttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#mediahttp://www.physicsclassroom.com/Class/sound/u11l2a.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2d.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2d.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2d.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfm


11/56

very small deformation of shape (and dimension) when a stress is applied to it. Steel is

a rigid material with a high elasticity. On the other hand, a material such as a rubber

band is highly flexible; when a force is applied to stretch the rubber band, it deforms or

changes its shape readily. A small stress on the rubber band causes a large deformation.

Steel is considered to be a stiff or rigid material, whereas a rubber band is considered a

flexible material. At the particle level, a stiff or rigid material is characterized by atoms

and/or molecules with strong attractions for each other. When a force is applied in an

attempt to stretch or deform the material, its strong particle interactions prevent this

deformation and help the material maintain its shape. Rigid materials such as steel are

considered to have a high elasticity. (Elastic modulus is the technical term). The phase

of matter has a tremendous impact upon the elastic properties of the medium. In

general, solids have the strongest interactions between particles, followed by liquids

and then gases. For this reason, longitudinal sound waves travel faster in solids than

they do in liquids than they do in gases. Even though the inertial factor may favor gases,

the elastic factor has a greater influence on the speed (v) of a wave, thus yielding thisgeneral pattern:

vsolids> vliquids> vgases

Inertial properties are those properties related to the material's tendency to be sluggish

to changes in its state of motion. The density of a medium is an example of an inertial

property. The greater the inertia (i.e., mass density) of individual particles of the

medium, the less responsive they will be to the interactions between neighboring

particles and the slower that the wave will be. As stated above, sound waves travel

faster in solids than they do in liquids than they do in gases. However, within a single

phase of matter, the inertial property of density tends to be the property that has a

greatest impact upon the speed of sound. A sound wave will travel faster in a less

dense material than a more dense material. Thus, a sound wave will travel nearly three

times faster in Helium than it will in air. This is mostly due to the lower mass of Helium

particles as compared to air particles.

The speed of a sound wave in air depends upon the properties of the air, mostly the

temperature, and to a lesser degree, the humidity. Humidity is the result of water vapor

being present in air. Like any liquid, water has a tendency to evaporate. As it does,

particles of gaseous water become mixed in the air. This additional matter will affect

the mass density of the air (an inertial property). The temperature will affect the

strength of the particle interactions (an elastic property). At normal atmosphericpressure, the temperature dependence of the speed of a sound wave through dry airis

approximated by the following equation:

v = 331 m/s + (0.6 m/s/C)T


12/56

where T is the temperature of the air in degrees Celsius. Using this equation to

determine the speed of a sound wave in air at a temperature of 20 degrees Celsius

yields the following solution.

v = 331 m/s + (0.6 m/s/C)T

v = 331 m/s + (0.6 m/s/C)(20 C)

v = 331 m/s + 12 m/s

v = 343 m/s

(The above equation relating the speed of a sound wave in air to the temperature

provides reasonably accurate speed values for temperatures between 0 and 100 Celsius.

The equation itself does not have any theoretical basis; it is simply the result of

inspecting temperature-speed data for this temperature range. Other equations do exist

that are based upon theoretical reasoning and provide accurate data for all

temperatures. Nonetheless, the equation above will be sufficient for our use as

introductory Physics students.)

Human hearing relies on the ability of the ear and the neural system to sense andprocess variations in sound pressure. Accordingly, the act of hearing has bothsubconscious and conscious effects. Subconscious effects, such as hearing loss, aredue to prolonged exposure to high sound pressure levels. Conscious effects are adirect result of the ears' acute response to a sound and how the cognitive part ofthe brain evaluates the sound. An example of an acute response to a sound is thepain and resultant ringing felt in the ear when a whistle is blown close to the ear inan enclosed environment. An example of utilizing conscious response is using soundto convey information to consumers, such as designing a product to emit sounds

that indicate operation and/or status. Psychoacoustics is the field of study thatseeks to better understand our perception of sound by investigating its consciouseffects.

For speech and music, the verbal content conveys much of the information.Furthermore, for speech, music, and many other sounds, the physicalcharacteristics of the sound produce hearing sensations in the listener. The tablebelow lists three primary physical characteristics of sound and their correspondinghearing sensations.

Physical Characteristic Hearing Sensation

Sound Pressure Level Loudness

Frequency Pitch

Duration Subjective Duration


13/56

These three hearing sensations directly correlate with their corresponding physicalcharacteristic. However, human hearing is a complex system and many sensationsdo not correlate directly to one physical characteristic. For example, in the tableabove, the sensation of pitch is also dependent on the sound pressure level.

Much of the challenge in the field of psychoacoustics stems from the fact that

different listeners perceive identical sounds differently. Differences in age, gender,nationality, and many other factors affect human perception. In addition to thischallenge of a heterogeneous population, consumer expectations are different fordifferent types of products they purchase. For example, a customer expectsdifferent sound characteristics from motorcycles, dishwashers, and personalcomputers. Therefore, sound quality evaluations are usually specific to the type ofproduct and the target consumer.

Because hearing is one of the integral processes through which humans receiveinformation and because the sound of a product carries so much information, thereis significant, ongoing research to classify hearing sensations and correlate thesesensations to physical characteristics of the signal. Through ongoing investigation,

researchers continue to identify physical characteristics of interest and proposeimproved objective sound quality metrics that correlate better to human perception.

Physiology of Human Hearing

The ear is an organ that receives audible information and transmits that sound tothe neural system, which results in auditory sensations. However, the body of thelistener distorts the sound field. Researchers can measure the resultant change inthe sound field by calculating the difference between the sound pressure level inthe free field and the sound pressure level in the ear canal of the listener. The bodyof the listener changes the sound field the most for frequencies below 1.5 kHz.

Scientists typically divide the human ear into three main regions: the outer ear, the

middle ear, and the inner ear. The following figure shows a diagram of the humanear.


14/56

The outer ear canal, because of its shape and length, is responsible for the highsensitivity to sounds with frequency components around 4 kHz. The middle eartransfers sound energy from the oscillations of air particles in the outer ear to

oscillations in the fluids within the inner ear. The middle ear system acts like atransformer, matching the acoustic impedance between the air and the fluids atfrequencies centered at 1 kHz. The inner ear transmits the fluid oscillations to thecorti on the basilar membrane, where sensory cells convert the fluid oscillations tosignals that the nervous system can process. The inner ear also can separatefrequencies, because different frequencies produce maximum oscillations atdifferent positions along the basilar membrane.

Limits of Hearing

The ear is a very sophisticated auditory organ and can be thought of as a complexinstrument for auditory signals. Human hearing can detect small variations in airpressure, ranging from 10 Pa up to 100 Pa. The detection of these small variations

occurs in the presence of atmospheric pressure, where 1 atm = 101.3 kPa.Furthermore, humans perceive loudness on a logarithmic scale. The internationalstandard reference for sound pressure level measurements is 20 Pa (0 dB), whichis the threshold of quiet. This is considered the nominal threshold of hearing,although approximately half of the general population can sense sounds at evenlower levels. On the opposite end of sound pressure level measurements, humans

experience discomfort and pain from sounds with sound pressure levels greaterthan 100 Pa (134 dB). Within this range in level, humans can typically discernchanges as small as 1 dB.

Human hearing can detect frequencies between 20 Hz and 20 kHz. Frequencycomponents outside this range are not generally considered to impact the humanperception of sound, regardless of the sound pressure level. As explained in theprevious section, there are physical reasons why human hearing is most sensitiveto frequency components around 1 kHz and 4 kHz. Many studies have


15/56

demonstrated the sensitivity of the ear as a function of frequency, which is typicallyplotted in equal loudness curves as in the following figure.1

Besides the sound pressure level-dependent sensitivity of hearing, humans also candifferentiate very fine changes in frequency. Below frequencies of 500 Hz, the ear

can differentiate tone bursts with a frequency difference of approximately 1 Hz.Above 500 Hz, the barely-noticeable difference is proportional to the frequency(0.002 x f).

Masking

Masking describes the phenomenon in which a sound becomes imperceptible due tothe presence of another sound. An example of this phenomenon is when loud musicmasks the sound of emergency sirens, or when a background noise partially masks

conversational speech. The transition between an unmasked tone and a completelymasked tone is continuous. The masked threshold is the sound pressure level of abarely-audible test tone in the presence of a masking sound.

Time Masking

Simultaneous masking describes the effect when the masked signal and the

masking signal occur at the same time. Human hearing is sensitive to the temporalstructure of sound, and masking also can occur between sounds that are notpresent simultaneously. Pre-masking is when the test tone occurs before themasking sound. Post-masking is when the test tone occurs after the masking sound.The following figure shows the time regions of pre-masking, simultaneous masking,and post-masking in relation to the masking signal.


16/56

Post-masking is a pronounced phenomenon that corresponds to decay in the effectof the masking signal. Pre-masking is a more subtle effect caused by the fact thathearing does not occur instantaneously because sounds require some time to sense.As indicated in the figure above, researchers typically can measure pre-masking foronly about 20 ms. Post-masking is the more dominant temporal effect and can bemeasured for 100 ms following the cessation of the masking sound. Both thethreshold in quiet and the masked threshold depend on the duration of the testtone. Researchers must know these dependencies when investigating pre- andpost-masking because they use short-duration test signals to perform thesemeasurements.

Frequency Masking

Broadband white noise can mask test tones. White noise has a spectral density thatis independent of frequency. Other types of noise and signals, such as pink noise,narrow-band noise, pure tones, and complex tones, also can mask a test signal.When narrow-band noise is the masking signal, masked thresholds show a verysteep rise greater than 100 dB per decade as the test tone increases in frequency

up to the center frequency of the narrow-band noise. This test tone increase isindependent of the level of the masking noise. For frequencies greater than thecenter frequency of the noise, the masked threshold decreases quickly for lowlevels of masking noise but more slowly for high levels of masking noise. Whenpure tones are the masking signal, the signal needs additional filters to removemeasurement artifacts such as audible beating and difference tones. The followingfigure shows the masked threshold for a masking signal at a frequency of 1 kHz.

Guitara stringed instrument usually having six strings

Octave

a set of 8 notes

Fiftha set of 5 notes

Fourtha set of 4 notes


17/56

Thirda set of 3 notes

Seconda set of 2 notes

Sixtha set of 6 notes

Seventha set of 7 notes

Node

a place where no sound waves are generated

Theme Movement #2 New World Symphonythe required piece for 2013 Science Olympiad

Sound Wavea wave that transmits sound

Standing wavea wave (as a sound wave in a chamber or an

electromagnetic wave in a transmission line) inwhich the ratio of its instantaneous amplitude atone point to that at any other point does not vary

with time

HertzThe unit of frequency

Percussion InstrumentAn instrument that you pound on a piece tomake it generate sound waves.

Wind InstrumentAn instrument that you blow into to make sound

Brass InstrumentAn wind instrument made of brass


18/56

String Instrument

An instrument that uses string vibrations tocreate sound waves.

Pitchthe property of sound that varies with variationin the frequency of vibration

Speed of SoundThe speed at which a sound wave travels (340.29meters per second at sea level)

Timbrethe distinctive property of a complex sound

Wave interferenceis the phenomenon that occurs when two waves meet whiletraveling along the same medium. The interference of waves causes the medium to

take on a shape that results from the net effect of the two individual waves upon the

particles of the medium. As mentioned ina previous unitof The Physics Classroom

Tutorial, if two upward displaced pulses having the same shape meet up with one

another while traveling in opposite directions along a medium, the medium will take on

the shape of an upward displaced pulse with twice the amplitude of the two interfering

pulses. This type of interference is known as constructive interference. If an upward

displaced pulse and a downward displaced pulse having the same shape meet up with

one another while traveling in opposite directions along a medium, the two pulses will

cancel each other's effect upon the displacement of the medium and the medium will

assume the equilibrium position. This type of interference is known as destructive

interference. The diagrams below show two waves - one is blue and the other is red -

interfering in such a way to produce a resultant shape in a medium; the resultant is

shown in green. In two cases (on the left and in the middle), constructive interference

occurs and in the third case (on the far right, destructive interference occurs.

But how can sound waves that do not possess upward and downward displacements

interfere constructively and destructively? Sound is a pressure wave that consists

ofcompressionsandrarefactions.As a compression passes through a section of a
http://www.physicsclassroom.com/Class/waves/u10l3c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l3c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l3c.cfmhttp://www.physicsclassroom.com/Class/sound/u11l1c.cfm#candphttp://www.physicsclassroom.com/Class/sound/u11l1c.cfm#candphttp://www.physicsclassroom.com/Class/sound/u11l1c.cfm#candphttp://www.physicsclassroom.com/Class/sound/u11l1c.cfm#candphttp://www.physicsclassroom.com/Class/sound/u11l1c.cfm#candphttp://www.physicsclassroom.com/Class/sound/u11l1c.cfm#candphttp://www.physicsclassroom.com/Class/sound/u11l1c.cfm#candphttp://www.physicsclassroom.com/Class/sound/u11l1c.cfm#candphttp://www.physicsclassroom.com/Class/waves/u10l3c.cfm


19/56

medium, it tends to pull particles together into a small region of space, thus creating a

high-pressure region. And as a rarefaction passes through a section of a medium, it

tends to push particles apart, thus creating a low-pressure region. The interference of

sound waves causes the particles of the medium to behave in a manner that reflects

the net effect of the two individual waves upon the particles. For example, if a

compression (high pressure) of one wave meets up with a compression (high pressure)

of a second wave at the same location in the medium, then the net effect is that that

particular location will experience an even greater pressure. This is a form of

constructive interference. If two rarefactions (two low-pressure disturbances) from two

different sound waves meet up at the same location, then the net effect is that that

particular location will experience an even lower pressure. This is also an example of

constructive interference. Now if a particular location along the medium repeatedly

experiences the interference of two compressions followed up by the interference of

two rarefactions, then the two sound waves will continually reinforceeach other and

produce a very loud sound. The loudness of the sound is the result of the particles atthat location of the medium undergoing oscillations from very high to very low

pressures. As mentioned ina previous unit,locations along the medium where

constructive interference continually occurs are known as anti-nodes. The animation

below shows two sound waves interfering constructively in order to produce very large

oscillations in pressure at a variety of anti-nodal locations. Note that compressions are

labeled with a C and rarefactions are labeled with an R.

Now if two sound waves interfere at a given location in such a way that the

compression of one wave meets up with the rarefaction of a second wave, destructive

interference results. The net effect of a compression (which pushes particles together)

and a rarefaction (which pulls particles apart) upon the particles in a given region of the

medium is to not even cause a displacement of the particles. The tendency of the

compression to push particles together is canceled by the tendency of the rarefactions

to pull particles apart; the particles would remain at their rest position as though there

wasn't even a disturbance passing through them. This is a form of destructive

interference. Now if a particular location along the medium repeatedly experiences the

interference of a compression and rarefaction followed up by the interference of ararefaction and a compression, then the two sound waves will continually canceleach

other and no sound is heard. The absence of sound is the result of the particles

remaining at rest and behaving as though there were no disturbance passing through it.

Amazingly, in a situation such as this, two sound waves would combine to produce no

sound. As mentioned ina previous unit,locations along the medium where destructive

interference continually occurs are known as nodes.
http://www.physicsclassroom.com/Class/waves/u10l4c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l4c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l4c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l4c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l4c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l4c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l4c.cfmhttp://www.physicsclassroom.com/Class/waves/u10l4c.cfm


20/56

Two Source Sound Interference

A popular Physics demonstration involves the interference of two sound waves from two

speakers. The speakers are set approximately 1-meter apart and produced identical

tones. The two sound waves traveled through the air in front of the speakers, spreading

our through the room in spherical fashion. A snapshot in time of the appearance of

these waves is shown in the diagram below. In the diagram, the compressions of a

wavefront are represented by a thick line and the rarefactions are represented by thin

lines. These two waves interfere in such a manner as to produce locations of some loud

sounds and other locations of no sound. Of course the loud sounds are heard at

locations where compressions meet compressions or rarefactions meet rarefactions and

the "no sound" locations appear wherever the compressions of one of the waves meet

the rarefactions of the other wave. If you were to plug one ear and turn the other ear

towards the place of the speakers and then slowly walk across the room parallel to theplane of the speakers, then you would encounter an amazing phenomenon. You would

alternatively hear loud sounds as you approached anti-nodal locations and virtually no

sound as you approached nodal locations. (As would commonly be observed, the nodal

locations are not true nodal locations due to reflections of sound waves off the walls.

These reflections tend to fill the entire room with reflected sound. Even though the

sound waves that reach the nodal locations directly from the speakers destructively

interfere, other waves reflecting off the walls tend to reach that same location to

produce a pressure disturbance.)

Destructive interference of sound waves becomes an important issue in the design ofconcert halls and auditoriums. The rooms must be designed in such as way as to

reduce the amount of destructive interference. Interference can occur as the result of

sound from two speakers meeting at the same location as well as the result of sound

from a speaker meeting with sound reflected off the walls and ceilings. If the sound

arrives at a given location such that compressions meet rarefactions, then destructive

interference will occur resulting in a reduction in the loudness of the sound at that
http://www.physicsclassroom.com/mmedia/waves/ipl.cfmhttp://www.physicsclassroom.com/mmedia/waves/ipl.cfm


21/56

location. One means of reducing the severity of destructive interference is by the design

of walls, ceilings, and baffles that serve to absorb sound rather than reflect it. This will

be discussed in more detaillater in Lesson 3.

The destructive interference of sound waves can also be used advantageously in noise

reduction systems. Earphones have been produced that can be used by factory andconstruction workers to reduce the noise levels on their jobs. Such earphones capture

sound from the environment and use computer technology to produce a second sound

wave that one-half cycle out of phase. The combination of these two sound waves within

the headset will result in destructive interference and thus reduce a worker's exposure

to loud noise.

Musical Beats and Intervals

Interference of sound waves has widespread applications in the world of music. Musicseldom consists of sound waves of a single frequency played continuously. Few music

enthusiasts would be impressed by an orchestra that played music consisting of the

note with a pure tone played by all instruments in the orchestra. Hearing a sound wave

of 256 Hz (middle C) would become rather monotonous (both literally and figuratively).

Rather, instruments are known to produce overtones when played resulting in a sound

that consists of a multiple of frequencies. Such instruments are described as being rich

in tone color. And even the best choirs will earn their moneywhen two singers sing two

notes (i.e., produce two sound waves) that are anoctave apart.Music is a mixture of

sound waves that typically have whole number ratios between the frequencies

associated with their notes. In fact, the major distinction between music and noise isthat noise consists of a mixture of frequencies whose mathematical relationship to one

another is not readily discernible. On the other hand, music consists of a mixture of

frequencies that have aclear mathematical relationshipbetween them. While it may be

true that "one person's music is another person's noise" (e.g., your music might be

thought of by your parents as being noise), a physical analysis of musical sounds

reveals a mixture of sound waves that are mathematically related.

To demonstrate this nature of music, let's consider one of the simplest mixtures of two

different sound waves - two sound waves with a 2:1 frequency ratio. This combination

of waves is known as an octave. A simple sinusoidal plot of the wave pattern for twosuch waves is shown below. Note that the red wave has two times the frequency of the

blue wave. Also observe that the interference of these two waves produces a resultant

(in green) that has a periodic and repeating pattern. One might say that two sound

waves that have a clear whole number ratio between their frequencies interfere to

produce a wave with a regular and repeating pattern. The result is music.
http://www.physicsclassroom.com/Class/sound/u11l3c.cfm#acousticshttp://www.physicsclassroom.com/Class/sound/u11l3c.cfm#acousticshttp://www.physicsclassroom.com/Class/sound/u11l3c.cfm#acousticshttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l3c.cfm#acoustics


22/56

Another simple example of two sound waves with a clear mathematical relationship

between frequencies is shown below. Note that the red wave has three-halves the

frequency of the blue wave. In the music world, such waves are said to bea fifth

apartand represent a popular musical interval. Observe once more that the interference

of these two waves produces a resultant (in green) that has a periodic and repeating

pattern. It should be said again: two sound waves that have a clear whole number ratio

between their frequencies interfere to produce a wave with a regular and repeating

pattern; the result is music.

Finally, the diagram below illustrates the wave pattern produced by two dissonant or

displeasing sounds. The diagram shows two waves interfering, but this time there is

nosimplemathematical relationship between their frequencies (in computer terms, one

has a wavelength of 37 and the other has a wavelength 20 pixels). Observe (lookcarefully) that the pattern of the resultant is neither periodic nor repeating (at least not

in the short sample of time that is shown). The message is clear: if two sound waves

that have no simple mathematical relationship between their frequencies interfere to

produce a wave, the result will be an irregular and non-repeating pattern. This tends to

be displeasing to the ear.
http://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octavehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#octave


23/56


24/56

The beat frequencyrefers to the rate at which the volume is heard to be oscillating

from high to low volume. For example, if two complete cycles of high and low volumes

are heard every second, the beat frequency is 2 Hz. The beat frequency is always equal

to the difference in frequency of the two notes that interfere to produce the beats. So if

two sound waves with frequencies of 256 Hz and 254 Hz are played simultaneously, a

beat frequency of 2 Hz will be detected. A common physics demonstration involves

producing beats using two tuning forks with very similar frequencies. If a tine on one of

two identical tuning forks is wrapped with a rubber band, then that tuning forks

frequency will be lowered. If both tuning forks are vibrated together, then they produce

sounds with slightly different frequencies. These sounds will interfere to produce

detectable beats. The human ear is capable of detecting beats with frequencies of 7 Hz

and below.

A piano tuner frequently utilizes the phenomenon of beats to tune a piano string. She

will pluck the string and tap a tuning fork at the same time. If the two sound sources -

the piano string and the tuning fork - produce detectable beats then their frequencies

are not identical. She will then adjust the tension of the piano string and repeat the

process until the beats can no longer be heard. As the piano string becomes more in

tune with the tuning fork, the beat frequency will be reduced and approach 0 Hz. When

beats are no longer heard, the piano string is tuned to the tuning fork; that is, they play

the same frequency. The process allows a piano tuner to match the strings' frequency

to the frequency of a standardized set of tuning forks.

Suppose that there is a happy bug in the center of a circular water puddle. The bug is

periodically shaking its legs in order to produce disturbances that

travel through the water. If these disturbances originate at a

point, then they would travel outward from that point in all

directions. Since each disturbance is traveling in the same


25/56

medium, they would all travel in every direction at the same speed. The pattern

produced by the bug's shakingwould be a series of concentric circles as shown in the

diagram at the right. These circles would reach the edges of the water puddle at the

same frequency. An observer at point A (the left edge of the puddle) would observe the

disturbances to strike the puddle's edge at the same frequency that would be observed

by an observer at point B (at the right edge of the puddle). In fact, the frequency at

which disturbances reach the edge of the puddle would be the same as the frequency

at which the bug produces the disturbances. If the bug produces disturbances at a

frequency of 2 per second, then each observer would observe them approaching at a

frequency of 2 per second.

Now suppose that our bug is moving to the right across the puddle of water and

producing disturbances at the same frequency of 2 disturbances

per second. Since the bug is moving towards the right, each

consecutive disturbance originates from a position that is closer

to observer B and farther from observer A. Subsequently, eachconsecutive disturbance has a shorter distance to travel before

reaching observer B and thus takes less time to reach observer B.

Thus, observer B observes that the frequency of arrival of the

disturbances is higher than the frequency at which disturbances

are produced. On the other hand, each consecutive disturbance has a further distance

to travel before reaching observer A. For this reason, observer A observes a frequency

of arrival that is less than the frequency at which the disturbances are produced. The

net effect of the motion of the bug (the source of waves) is that the observer towards

whom the bug is moving observes a frequency that is higher than 2

disturbances/second; and the observer away from whom the bug is moving observes a

frequency that is less than 2 disturbances/second. This effect is known as the Doppler

effect.

The Doppler effect is observed whenever the source of waves is moving with respect to

an observer. The Doppler effectcan be described as the effect produced by a moving

source of waves in which there is an apparent upward shift in frequency for observers

towards whom the source is approaching and an apparent downward shift in frequency

for observers from whom the source is receding. It is important to note that the effect

does not result because of an actual change in the frequency of the source. Using the

example above, the bug is still producing disturbances at a rate of 2 disturbances persecond; it just appears to the observer whom the bug is approaching that the

disturbances are being produced at a frequency greater than 2 disturbances/second.

The effect is only observed because the distance between observer B and the bug is

decreasing and the distance between observer A and the bug is increasing.


26/56

The Doppler effect can be observed for any type of wave - water wave, sound wave,

light wave, etc. We are most familiar with the Doppler effect because of our

experiences with sound waves. Perhaps you recall an instance in which a police car or

emergency vehicle was traveling towards you on the highway. As the car approached

with its siren blasting, the pitch of the siren sound (a measure of the siren's frequency)

was high; and then suddenly after the car passed by, the pitch of the siren sound was

low. That was the Doppler effect - an apparent shift in frequency for a sound wave

produced by a moving source.

The Doppler effect is of intense interest to astronomers who use the information about

the shift in frequency of electromagnetic waves produced by moving stars in our galaxy

and beyond in order to derive information about those stars and galaxies. The belief

that the universe is expanding is based in part upon observations of electromagnetic

waves emitted by stars in distant galaxies. Furthermore, specific information about stars

within galaxies can be determined by application of the Doppler effect. Galaxies are

clusters of stars that typically rotate about some center of mass point. Electromagnetic

radiation emitted by such stars in a distant galaxy would appear to be shifted

downward in frequency (a red shift) if the star is rotating in its cluster in a direction that

is away from the Earth. On the other hand, there is an upward shift in frequency

(a blue shift) of such observed radiation if the star is rotating in a direction that is

towards the Earth.

As a wave travels through a medium, it will often reach the end of the medium and

encounter an obstacle or perhaps another medium through which it could travel.

Oneexampleof this has already been mentioned in Lesson 2. A sound wave is known to

reflect off canyon walls and other obstacles to produce an echo. A sound wave travelingthrough air within a canyon reflects off the canyon wall and returns to its original

source. What affect does reflection have upon a wave? Does reflection of a wave affect

the speed of the wave? Does reflection of a wave affect the wavelength and frequency

of the wave? Does reflection of a wave affect the amplitude of the wave? Or does

reflection affect other properties and characteristics of a wave's motion? The behavior

of a wave (or pulse) upon reaching the end of a medium is referred to as boundary
http://www.physicsclassroom.com/Class/waves/u10l2d.cfm#echohttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#echohttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#echo


27/56

behavior. When one medium ends, another medium begins; the interface of the two

media is referred to as the boundaryand the behavior of a wave at that boundary is

described as its boundary behavior. The questions that are listed above are the types of

questions we seek to answer when we investigate the boundary behavior of waves. the

behavior of waves traveling along a rope from a more dense medium to a less dense

medium (and vice versa) was discussed. The wave doesn't juststopwhen it reaches the

end of the medium. Rather, a wave will undergo certain behaviors when it encounters

the end of the medium. Specifically, there will be some reflection off the boundary and

some transmission into the new medium. But what if the wave is traveling in a two-

dimensional medium such as a water wave traveling through ocean water? Or what if

the wave is traveling in a three-dimensional medium such as a sound wave or a light

wave traveling through air? What types of behaviors can be expected of such two- and

three-dimensional waves?

The study of waves in two dimensions is often done using a

ripple tank. A ripple tank is a large glass-bottomed tank ofwater that is used to study the behavior of water waves. A

light typically shines upon the water from above and

illuminates a white sheet of paper placed directly below the

tank. A portion of light is absorbed by the water as it passes

through the tank. A crest of water will absorb more light than

a trough. So the bright spots represent wave troughs and the

dark spots represent wave crests. As the water waves move

through the ripple tank, the dark and bright spots move as

well. As the waves encounter obstacles in their path, their

behavior can be observed by watching the movement of the dark and bright spots on

the sheet of paper. Ripple tank demonstrations are commonly done in a Physics class in

order to discuss the principles underlying the reflection, refraction, and diffraction of

waves.

If a linear object attached to an oscillator bobs back and forth within the water, it

becomes a source of straightwaves. These straight waves have alternating crests and

troughs. As viewed on the sheet of paper below the tank, the crests are the dark lines

stretching across the paper and the troughs are the bright lines. These

waves will travel through the water until they encounter an obstacle -

such as the wall of the tank or an object placed within the water. Thediagram at the right depicts a series of straight waves approaching a

long barrier extending at an angle across the tank of water. The

direction that these wavefronts (straight-line crests) are traveling

through the water is represented by the blue arrow. The blue arrow is called a rayand

is drawn perpendicular to the wavefronts. Upon reaching the barrier placed within the

water, these waves bounce off the water and head in a different direction. The diagram


28/56

below shows the reflected wavefronts and the reflected ray. Regardless of the angle at

which the wavefronts approach the barrier, one general law of reflection holds true: the

waves will always reflect in such a way that the angle at which they approach the

barrier equals the angle at which they reflect off the barrier. This is known as the law

of reflection. This law will be discussed in more detail inUnit 13 of The Physics

Classroom.

The discussion above pertains to the reflection of waves off of straight

surfaces. But what if the surface is curved, perhaps in the shape of a

parabola? What generalizations can be made for the reflection of water

waves off parabolic surfaces? Suppose that a rubber tube having the

shape of a parabola is placed within the water. The diagram at the

right depicts such a parabolic barrier in the ripple tank. Several

wavefronts are approaching the barrier; the ray is drawn for these wavefronts. Upon

reflection off the parabolic barrier, the water waves will change direction and head

towards a point. This is depicted in the diagram below. It is as though all the energy

being carried by the water waves is converged at a single point - the point is known asthe focal point. After passing through the focal point, the waves spread out through the

water. Reflection of waves off of curved surfaces will be discussed in more detail in Unit

13 of The Physics Classroom.

Reflection involves a change in direction of waves when they bounce off a

barrier.Refractionof waves involves a change in the direction of waves as they pass

from one medium to another. Refraction, or the bending of the path of the waves, is

accompanied by a change in speed and wavelength of the waves. InLesson 2,it was
http://www.physicsclassroom.com/Class/refln/u13l1c.cfmhttp://www.physicsclassroom.com/Class/refln/u13l1c.cfmhttp://www.physicsclassroom.com/Class/refln/u13l1c.cfmhttp://www.physicsclassroom.com/Class/refln/u13l1c.cfmhttp://www.physicsclassroom.com/Class/refln/u13l3a.cfmhttp://www.physicsclassroom.com/Class/refln/u13l3a.cfmhttp://www.physicsclassroom.com/Class/refln/u13l3a.cfmhttp://www.physicsclassroom.com/Class/refln/u13l3a.cfmhttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#mediahttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#mediahttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#mediahttp://www.physicsclassroom.com/Class/waves/u10l2d.cfm#mediahttp://www.physicsclassroom.com/Class/refln/u13l3a.cfmhttp://www.physicsclassroom.com/Class/refln/u13l3a.cfmhttp://www.physicsclassroom.com/Class/refln/u13l1c.cfmhttp://www.physicsclassroom.com/Class/refln/u13l1c.cfm


29/56

mentioned that the speed of a wave is dependent upon the properties of the medium

through which the waves travel. So if the medium (and its properties) is changed, the

speed of the waves is changed. The most significant property of water that would affect

the speed of waves traveling on its surface is the depth of the water. Water waves

travel fastest when the medium is the deepest. Thus, if water waves are passing from

deep water into shallow water, they will slow down. And as mentioned inthe previous

section of Lesson 3,this decrease in speed will also be accompanied by a decrease in

wavelength. So as water waves are transmitted from deep water into shallow water,

the speed decreases, the wavelength decreases, and the direction

changes.

This boundary behavior of water waves can be observed in a ripple

tank if the tank is partitioned into a deep and a shallow section. If a

pane of glass is placed in the bottom of the tank, one part of the tank

will be deep and the other part of the tank will be shallow. Waves

traveling from the deep end to the shallow end can be seen to refract (i.e., bend),decrease wavelength (the wavefronts get closer together), and slow down (they take a

longer time to travel the same distance). When traveling from deep water to shallow

water, the waves are seen to bend in such a manner that they seem to be traveling

more perpendicular to the surface. If traveling from shallow water to deep water, the

waves bend in the opposite direction. The refraction of light waves will be discussed in

more detail ina later unit of The Physics Classroom.

Reflection involves a change in direction of waves when they bounce off a

barrier;refractionof waves involves a change in the direction of waves

as they pass from one medium to another; and diffractioninvolves a

change in direction of waves as they pass through an opening or

around a barrier in their path. Water waves have the ability to travel

around corners, around obstacles and through openings. This ability is

most obvious for water waves with longer wavelengths. Diffraction can

be demonstrated by placing small barriers and obstacles in a ripple

tank and observing the path of the water waves as they encounter the obstacles. The

waves are seen to pass around the barrier into the regions behind it; subsequently the

water behind the barrier is disturbed. The amount of diffraction (the sharpness of thebending) increases with increasing wavelength and decreases with decreasing

wavelength. In fact, when the wavelength of the waves is smaller than the obstacle, no

noticeable diffraction occurs.

Diffraction of water waves is observed in a harbor as waves bend around small boats

and are found to disturb the water behind them. The same waves however are unable

to diffract around larger boats since their wavelength is smaller than the boat.
http://www.physicsclassroom.com/Class/waves/u10l3a.cfm#lambdahttp://www.physicsclassroom.com/Class/waves/u10l3a.cfm#lambdahttp://www.physicsclassroom.com/Class/waves/u10l3a.cfm#lambdahttp://www.physicsclassroom.com/Class/waves/u10l3a.cfm#lambdahttp://www.physicsclassroom.com/Class/refrn/http://www.physicsclassroom.com/Class/refrn/http://www.physicsclassroom.com/Class/refrn/http://www.physicsclassroom.com/Class/refrn/http://www.physicsclassroom.com/Class/waves/u10l3a.cfm#lambdahttp://www.physicsclassroom.com/Class/waves/u10l3a.cfm#lambda


30/56

Diffraction of sound waves is commonly observed; we notice sound diffracting around

corners, allowing us to hear others who are speaking to us from adjacent rooms. Many

forest-dwelling birds take advantage of the diffractive ability of long-wavelength sound

waves. Owls for instance are able to communicate across long distances due to the fact

that their long-wavelength hootsare able to diffract around forest trees and carry

farther than the short-wavelength tweetsof songbirds. Diffraction is observed of light

waves but only when the waves encounter obstacles with extremely small wavelengths

(such as particles suspended in our atmosphere). Diffraction ofsound wavesand

oflight waveswill be discussed in a later unit ofThe Physics Classroom Tutorial.

Reflection, refraction and diffraction are all boundary behaviors of waves associated

with the bending of the path of a wave. The bending of the path is an observable

behavior when the medium is a two- or three-dimensional medium. Reflection occurs

when there is a bouncing off of a barrier. Reflection of waves off straight barriersfollows the law of reflection. Reflection of waves off parabolic barriers results in the

convergence of the waves at a focal point. Refraction is the change in direction of

waves that occurs when waves travel from one medium to another. Refraction is always

accompanied by a wavelength and speed change. Diffraction is the bending of waves

around obstacles and openings. The amount of diffraction increases with increasing

wavelength.

The Bernoulli effect, or the Bernoulli principle or Bernoulli's law, is a statement of relationship

between flow speed and pressure in a fluid system; in essence, when the speed of horizontal flow

through a fluid increases, the pressure decreases. This effect, and the principle which states this

formally, was discovered by the renowned mathematician Daniel Bernoulli, who first published itsformulation in 1738. Since the word "fluid" inphysicsrefers to the behavior of both liquids and

gasses, such as air, the Bernoulli effect can be observed in both hydrodynamic, or fluid, systems as

well as aerodynamic, or gaseous, systems.

A common example used to explain the Bernoulli effect is the flow of fluid through a pipe. If the fluid

is moving uniformly through the pipe, then the only forces acting on the fluid are its own weight and

the pressure of the fluid itself. Now, if the pipe narrows, the fluid must speed up, because the same

amount of fluid is traveling through a smaller space. However, if the fluid is moving uniformly, and

the weight has not changed, then the only way in which the fluid will move faster is if the pressure

behind the fluid is greater than the pressure in front. Thus, the pressure must decrease as the speed

increases.

As has beenpreviously mentionedin this unit, a sound wave is created as a result of a

vibrating object. The vibrating object is the source of the disturbance that moves

through the medium. The vibrating object that creates the disturbance could be the

vocal cords of a person, the vibrating string and soundboard of a guitar or violin, the

vibrating tines of a tuning fork, or the vibrating diaphragm of a radio speaker. Any

object that vibrates will create a sound. The sound could be musical or it could be noisy;

but regardless of its quality, the sound wave is created by a vibrating object.
http://www.physicsclassroom.com/Class/sound/u11l3d.cfm#diffrnhttp://www.physicsclassroom.com/Class/sound/u11l3d.cfm#diffrnhttp://www.physicsclassroom.com/Class/sound/u11l3d.cfm#diffrnhttp://www.physicsclassroom.com/Class/light/http://www.physicsclassroom.com/Class/light/http://www.physicsclassroom.com/Class/index.cfmhttp://www.physicsclassroom.com/Class/index.cfmhttp://www.physicsclassroom.com/Class/index.cfmhttp://www.wisegeek.org/what-is-physics.htmhttp://www.wisegeek.org/what-is-physics.htmhttp://www.wisegeek.org/what-is-physics.htmhttp://www.physicsclassroom.com/Class/sound/u11l2a.cfmhttp://www.physicsclassroom.com/Class/sound/u11l2a.cfmhttp://www.physicsclassroom.com/Class/sound/u11l2a.cfmhttp://www.physicsclassroom.com/Class/sound/u11l2a.cfmhttp://www.wisegeek.org/what-is-physics.htmhttp://www.physicsclassroom.com/Class/index.cfmhttp://www.physicsclassroom.com/Class/light/http://www.physicsclassroom.com/Class/sound/u11l3d.cfm#diffrn


31/56

Nearly all objects, when hit or struck or plucked or strummed or somehow disturbed,

will vibrate. If you drop a meter stick or pencil on the floor, it will begin to vibrate. If

you pluck a guitar string, it will begin to vibrate. If you blow over the top of a pop

bottle, the air inside will vibrate. When each of these objects vibrates, they tend to

vibrate at a particular frequency or a set of frequencies. The frequency or frequencies

at which an object tends to vibrate with when hit, struck, plucked, strummed or

somehow disturbed is known as the natural frequencyof the object. If the

amplitudes of the vibrations are large enough and if natural frequency is within

thehuman frequency range,then the vibrating object will produce sound waves that

are audible.

All objects have a natural frequency or set of frequencies at which they vibrate. The

quality or timbreof the sound produced by a vibrating object is dependent upon the

natural frequencies of the sound waves produced by the objects. Some objects tend to

vibrate at a single frequency and they are often said to produce a pure tone. A flute

tends to vibrate at a single frequency, producing a very pure tone. Other objects vibrateand produce more complex waves with a set of frequencies that have awhole number

mathematical relationshipbetween them; these are said to produce a rich sound. A

tuba tends to vibrate at a set of frequencies that are mathematically related by whole

number ratios; it produces a rich tone. Still other objects will vibrate at a set of multiple

frequencies that have no simple mathematical relationship between them. These

objects are not musical at all and the sounds that they create could be described

asnoise.When a meter stick or pencil is dropped on the floor, it vibrates with a number

of frequencies, producing a complex sound wave that is clanky and noisy.

The actual frequency at which an object will vibrate at is determined by a variety of

factors. Each of these factors will either affect the wavelength or the speed of the

object. Since

frequency = speed/wavelength
http://www.physicsclassroom.com/Class/sound/u11l2a.cfm#rangehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#rangehttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#rangehttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#musichttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#musichttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#musichttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#musichttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#noisehttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#noisehttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#noisehttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#noisehttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#musichttp://www.physicsclassroom.com/Class/sound/u11l3a.cfm#musichttp://www.physicsclassroom.com/Class/sound/u11l2a.cfm#range


32/56

an alteration in either speed or wavelength will result in an alteration of the natural

frequency. The role of a musician is to control these variables in order to produce a

given frequency from the instrument that is being played. Consider a guitar as an

example. There are six strings, each having a different linear density (the wider strings

are more dense on a per meter basis), a different tension (which is controllable by the

guitarist), and a different length (also controllable by the guitarist). The speed at which

waves move through the strings isdependent upon the properties of the medium- in

this case the tightness (tension) of the string and the linear density of the strings.

Changes in these properties would affect the natural frequency of the particular string.

The vibrating portion of a particular string can be shortenedby pressing the string

against one of the frets on the neck of the guitar. This modification in the length of the

string would affect the wavelength of the wave and in turn the natural frequency at

which a particular string vibrates at. Controlling the speed and the wavelength in this

manner allows a guitarist to control the natural frequencies of the vibrating object (a

string) and thus produce the intended musical sounds. The same principles can beapplied to any string instrument - whether it is the harp, harpsichord, violin or guitar.

As another example, consider the trombone with its long cylindrical tube that is bent

upon itself twice and ends in a flared end. The trombone is an example of a wind

instrument. The tubeof any wind instrument acts as a container for a vibrating air

column. The air inside the tube will be set into vibration by a vibrating reed or the

vibrations of a musician's lips against a mouthpiece. While the speed of sound waves

within the air column is not alterable by the musician (they can only be altered

bychanges in room temperature), the length of the air column is. For a trombone, the

length is altered by pushing the tube outward away from the mouthpiece to lengthen it

or pulling it in to shorten it. This causes the length of the air column to be changed,

and subsequently changes the wavelength of the waves it produces. And of course, a

change in wavelength will result in a change in the frequency. So the natural frequency

of a wind instrument such as the trombone is dependent upon the length of the air

column of the instrument. The same principles can be applied to any similar instrument

(tuba, flute, wind chime, organ pipe, clarinet, or pop bottle) whose sound is produced

by vibrations of air within a tube.

There were a variety of classroom demonstrations (some of which are

fun

sounds of music study guide

Documents