Physics 1251 The Science and Technology of Musical Sound

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Physics 1251The Science and Technology of
Musical Sound

• Unit 2
• Session 17 MWF
• The Wave Properties Propagation and Addition

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Physics 1251 Unit 2 Session 17 Propagation
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• Foolscap Quiz
• A jet airplane flies over you at an altitude of
• 10 km. If the Sound Intensity Level 10
  meters from the engine is 120 dB ( 1 W/m2), what
  is the SIL ( or intensity) you hear?

Answer 60 dB. (1 x 10 -6 W/m2). SIL SIL0 20
Log (d /d0 ) SIL 120 dB 20 Log(10 000/10)
120 20 x 3 120 60 60 dB
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Physics 1251 Unit 2 Session 17 Propagation
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• 1' Lecture
• Wave motion is characterized by
• Reflection
• Refraction
• Diffraction
• Doppler Shift
• Beats
• Interference

The Reflective Ref Differed Dopily, Beating
Interference.
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Physics 1251 Unit 2 Session 17 Propagation
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• When the surface is smooth we have specular
  (mirror-like) reflection.

Reflection
Smooth Surface Roughness ? ?
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Physics 1251 Unit 2 Session 17 Propagation
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• Examples of Acoustic Reflection

• Echoes

• Band Shells

• Reverberations

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• What happens when a wave hits a change in the
  medium?

Reflection
Tin Tout
Tout
Tout
Tin
Tin
Transmission
Medium 1
Medium 2
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Physics 1251 Unit 2 Session 17 Propagation
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• What if the surface is rough?

Diffuse Reflection
Rough Surface Roughness gt ?
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Physics 1251 Unit 2 Session 17 Propagation
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• Reflection
• 80/20Reflection, a bouncing back, occurs
  whenever there is an abrupt change in the medium.

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• Refraction occurs when a wave enters a medium
  that has a different velocity.

Refraction
V1 lt V2
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• In the second medium the wavefront races ahead,
  changing the direction.

Refraction
V1
V2
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• Refraction
• When a band marches around a corner the marchers
  on the outside must march faster than those on
  the inside.

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Refraction Parade Analogy
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• Thought question
• What happens to a sound wave when the wind is
  blowing?

• If there is a wind shear,
• then refraction will occur.

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• Wind Speed Refraction
• velocity varies along wavefront

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• The Mystery of the
• Silent Lightening

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• Cold aloft
• v - slower Refraction
• velocity varies with
  temperature
• v - faster
• Warm below

v 343 0.6 (T- 20C)
silence
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Physics 1251 Unit 2 Session 17 Propagation
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• Refraction
• 80/20Refraction, a bending aside, occurs
  whenever there is a change in velocity along the
  wavefront.

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Physics 1251 Unit 2 Session 17 Propagation
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• What happens when a wave is partially obstructed?

Diffraction
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Physics 1251 Unit 2 Session 17 Propagation
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• Diffraction
• 80/20Diffraction, a bending around obstacles
  because every point on a wave is a source waves
  cannot terminate abruptly.

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Physics 1251 Unit 2 Session 17 Propagation
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• 80/20Huygens Principle every point on the wave
  is the source of a new (spherical) wavelet.

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• How can you hear someone who is around a corner?

Diffraction
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Doppler Shift Moving source
Higher f
Lower f
fobserver fsource v vobserver / v
vsource
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• Doppler Shift
• 80/20The Doppler shift is the change in the
  frequency of a source fsource observed fobserved
  due to the relative velocity of the source
  vsource , observer vobserver ,where the velocity
  of sound in the still medium is v.f observed f
  source ? v vobserver / v - vsource

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Physics 1251 Unit 2 Session 17 Propagation
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• Addition of Waves
• 80/20Coherent addition is the addition of the
  amplitudes of waves of the same frequency. The
  intensity then is proportional to the square of
  the the combined amplitude.
• Icoherent (a1 a2 )2 a12 a2 2 2a1a2

• 80/20Incoherent addition of waves is equal to
  the sum of their independent intensities if they
  are not within the critical bandwidth.
• Iincoherent a12 a2 2

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Physics 1251 Unit 2 Session 17 Propagation
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• Beats
• 80/20Beats are a modulation of intensity of due
  to the coherent addition of two sound waves whose
  frequency lie with a critical band width of each
  other.

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Physics 1251 Unit 2 Session 17 Propagation
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• Beat Frequency
• 80/20Two tones of frequency f1 and f2 sound like
  one tone of mean frequency
• f mean (f1 f 2)/2
• that beats at a beat frequency of
• f beat f1 f2 .

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Physics 1251 Unit 2 Session 17 Propagation
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Beats f1 f2
In phase
Out of phase
fmean
fbeat
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• Tuning a Guitar by Beats
• 80/20Two tones of frequency f1 and f2 sound like
  one tone of mean frequency
• f mean (f1 f 2)/2
• that beats at a beat frequency of
• f beat f1 f2 .

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Physics 1251 Unit 2 Session 17 Propagation
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• Interference
• 80/20Interference is the coherent addition of
  waves at various points in space that leads to
  modulation of the intensity in space.

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Physics 1251 Unit 2 Session 17 Propagation
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Interference
Constructive
Destructive
Softer
Louder
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• Summary
• Reflection is the return of a wave from a change
  in a medium.
• Refraction is bending of the wave due to velocity
  variation along the wavefront.
• Diffraction is the bending of the wave around
  obstacles because of Huygens Principle.
• Doppler Shift is the change in frequency due to
  the relative motion.

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Physics 1251 Unit 2 Session 17 Propagation
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• Summary
• Beats are intensity modulations in time due to
  coherent addition of waves of near equal
  frequency.
• Interference is spatial modulation of intensity
  due to the coherent addition of nearly equal
  frequency waves at different points in space.