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Sound, Wavefronts
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Wavefronts join points in phase
Linear wavefronts
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Wavefronts for compressional wave.
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Rays – a ray is an arrow sketched through the wave fronts (perpendicular) to show direction of wave propagation.
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Waves transfer energyEnergy is proportionalto the amplitude.
Less energy
More energy
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For light increased amplitude increases brightness.
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For sound: increased amplitude increases volume.
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What does wave frequency (f) determine?
Wave type for EM waves.
Color for light.
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Sound velocity solid
liquid
gas
In gas
hot faster.
cold slower.
Increasing velocity
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The Doppler Effect
Stationary Source Emitting Waves all Directions. Circular wavefronts have = & f.
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Doppler Effect from Moving Source
In front of source is less, behind is longer.
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Another View
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In front of source -short higher f:
hear higher pitch sound-see shorter light (blue).
behind source - longer lower f:
hear lower pitch soundsee longer light (red).
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When objects are in relative motion:
a) Toward each other, f received increases.
b) Away from each other, f received decreases.
Doppler Effect
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Resonance & Sympathetic Vibration
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All objects have a naturalAll objects have a natural
frequency of vibration.frequency of vibration.
ResonanceResonance - the inducing- the inducingof vibrations of a naturalof vibrations of a naturalrate by a vibrating sourcerate by a vibrating source
having the same frequencyhaving the same frequency
““sympathetic vibrations”sympathetic vibrations”
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Push at natural frequency, amplitude increases
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Resonance:
An oscillatory system that is driven by a force with a frequency = to its natural frequency.
System will resonate – amplitude will increase.
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Resonance & Sympathetic Vibration
Resonance occurs when a wave is in vicinity of an object & is vibrating at the natural frequency of the object. Object vibrates sympathetically at same frequency.
Continued vibration causes amplitude to increase.
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mechanical universe resonance
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A broad variety of tone colors exist because most sounds we perceive as pitch contain many frequencies.
• The predominant pitch The predominant pitch is called the is called the fundamental fundamental frequency. It is the frequency. It is the longest longest that forms a that forms a standing wave.standing wave.
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Standing Wave patterns form notes.
Each string or pipe vibrates with particular frequencies of standing waves.
Other frequencies tend to die out.
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Although we would perceive a string vibrating as a whole,
it vibrates in a pattern that appears erratic producing many different overtone pitches. What results are particular tone colors or timbres of instruments and voices.
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Waveform with overtones.
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Frequencies which occur along with the primary note are called the harmonic or overtone series.
When C is the fundamental the pitches below represent its first 15 overtones.
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There are several standing waves which can be produced by vibrations on a string, or rope. Each pattern corresponds to vibrations which occur at a particular frequency and is known as a harmonic.
Harmonics
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The lowest possible frequency at which a string could vibrate to form a standing wave pattern is known as the fundamental frequency or the first harmonic.
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2nd Harmonic
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Which One??
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String Length L, & Harmonics
Standing waves can form on a string of length L, when the can = ½ L, or 2/2 L, or 3/2L etc.
Standing waves are the overtones or harmonics.
L = nn. n = 1, 2, 3, 4 harmonics. 2
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Harmonic Frequencies
form where ½ can fit the string exactly.To calculate f:
L
nvf
2
f
vfv
2
nL
Substitute v/f for .
f
nvL
2
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1st standing wave forms when = 2LFirst harmonic frequency is when n = 1 as below.
L
nvf
21
When n = 1 f is fundamental frequency or 1st harmonic.
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L
nvf
22 For second harmonic n = 2.
f2 = v/L
Other standing waves with smaller wavelengths form other frequencies that ring out along with the fundamental.
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In general,
The harmonic frequencies can be found where n = 1,2,3… and n corresponds to the harmonic. v is the velocity of the wave on the string. L is the string length.
L
nvfn 2
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It is helpful to note that the distance between nodes on a standing wave is ½ .
½
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Pipes and Air Columns
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A resonant air column isA resonant air column issimply a standing simply a standing
longitudinallongitudinalwave system, much likewave system, much like
standing waves on a standing waves on a string.string. closed-pipe resonatorclosed-pipe resonator tube in which one end is tube in which one end is
openopenand the other end is closedand the other end is closed
open-pipe resonatoropen-pipe resonatortube in which both endstube in which both ends
are openare open
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Open Pipe – open end has antinode.
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Standing Waves in Open PipeBoth ends must be antinodes.
How much of the wavelength is the fundamental?
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The 1st harmonic or fundamental can fit ½ into the tube.
Just like the string L = n 2
fn = nv2L
Where n, the harmonic is an integer.
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Closed pipes must have a node at closed end and an antinode at the open end.
How many wavelengths??
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Here is the next harmonic.How many ’s?
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There are only odd harmonics possible.
L = 1/4.L = 3/4.L = 5/4
fn = nv where n = 1,3,5 … 4L
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Beats – caused by constructive & destructive interference from 2
frequency sounds interacting.
• Beat Frequency heard is the difference between 2 frequencies.
• If a 50 Hz wave and a 60 Hz wave overlap, you hear beat of 10 Hz.
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Traveling Waves Beats
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Holt read 13 - 3
pg 509 38 - 39, 41, 44 46, 47 pg 499 #1 – 4
Start in class finish for hwk.