Physics 1710 Chapter 17 Sound

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Physics 1710Chapter 17 Sound

• Quiz
• A piano tuner is tightening the tuning post on a
  piano. He tightens until there is 980. N of
  force on a string that has a mass density of
  0.0500 kg/m. When he plucks the string, how fast
  will the wave travel down the string? Is it
  sound?

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Physics 1710Chapter 17 Sound

• 1' Lesson
• The speed of sound is equal to the square root
  of the ratio of the Bulk Modulus to the density
  of the media.
• Sound is a longitudinal wave that is
  characterized by a small displacement of the
  medium from equilibrium and a corresponding
  pressure fluctuation from the equilibrium
  pressure.
• The velocity of sound at 20 C and one atmosphere
  is 343 m/s.

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Physics 1710Chapter 17 Sound

• 1' Lesson
• The pressure amplitude is equal to the product
  of the displacement amplitude smax, the density
  ?, the angular frequency ?, and the velocity of
  sound v in the medium.
• The intensity of a sound wave is the power
  divided by the area over which it is spread.
• The Sound Intensity Level (SIL) ? is equal to
  ten times (10 x) the logarithm of the ratio of
  the intensity to the reference level of 1 pW/m
  2.
• The intensity in a spherical wave decreases as
  the inverse square of the distance from the
  source.

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Physics 1710Chapter 17 Sound

• 1' Lesson
• The Doppler Effect is a shift in the frequency
  of a source due to the relative motion of the
  source and observer.
• f ' (v vo )/(v vs) f

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Physics 1710Chapter 17 Sound

• Characteristics of Sound
• Wave motion is similar to coupled oscillators.
• Sound is a displacement and pressure wave
  originating from a mechanical vibration.
• Sound requires a medium to propagate.
• Air has mass. ( ? 1.29 gm/liter)
• Air has elasticity. B 152. N/m 2/.

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Physics 1710Chapter 17 Sound

• The Density of Air

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Physics 1710Chapter 17 Sound

• The Spring of Air

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Physics 1710Chapter 17 Sound

• Ball on an Air Spring

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Physics 1710Chapter 17 Sound

• Simple Harmonic Oscillator
• F - B (?V/V) ?A
• - B x ?A2/V
• F m d 2x/dt 2
• d 2x/dt 2 F/m
• d 2x/dt 2 - B x ?A2/mV
• x A cos ( ?t ?)
• ? ?A vB /mV
• ? ?1/vV

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Physics 1710Chapter 17 Sound

• Helmholtz Resonator
• m ?L ?A
• F - B (?V/V) ?A
• - B x ?A2/V
• F m d 2x/dt 2
• d 2x/dt 2 - B x ?A /(? LV)
• x A cos ( ?t ?)
• ? vB ?A /(?LV)
• ? ?v(?A /LV)

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Physics 1710Chapter 17 Sound

• Helmholtz Resonators
• And the Jug Band

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Physics 1710Chapter 17 Sound

• Speed of Sound
• Consider a small volume of a compressible medium
  ( eg. air).
• Mass ?m ? ?x ?A
• Force on the mass
• F ?P(x?x) - ?P(x-?x) ?A
• But ?P(x) B dV/? V
• B (ds ?A)/(?x ?A) B ds/?x
• F m d 2s/dt 2
• B ds/?x - ds/?x- ?A (? ?x ?A )(d 2s/dt 2)
• B (d 2s/dx 2 )?x ?A (? ?x ?A )(d 2s/dt 2)

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Physics 1710Chapter 17 Sound

• B (d 2s/dx 2) ? (d 2s/dt 2)
• (d 2s/dx 2) ?/B (d 2s/dt 2)
• v v(B/ ?)
• v (331 m/s)v(1 TC / 273C )
• At 20 C v 343 m/s
• v 343 0.60( TC 20 C)

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Physics 1710Chapter 17 Sound

• The Wave Function for Sound
• s smax cos(kx -?t)
• ?P ?Pmax sin(kx -?t)
• ?Pmax ?v ? smax

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Physics 1710Chapter 17 Sound

• Intensity of a Sound Wave
• I P/ A ½ ? v (? smax) 2
• I ?Pmax2/(2?v)

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Physics 1710Chapter 17 Sound

• Sound Intensity Level (dB)
• 10 Log (I / I o )
• I o 1.00 x 10 12 W/m 2
• 1.00 pW/m 2

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Physics 1710Chapter 17 Sound

• Inverse Square Law
• for Spherical Waves
• I Pave/A Pave/(4? r 2)

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Physics 1710Chapter 17 Sound

• Doppler Effect
• f ' f (v vo )/(v vs )

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Physics 1710Chapter 17 Sound

• Shock Waves

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Physics 1710Chapter 17 Sound

• Summary
• The speed of sound v v(B/ ?)
• Sound is a pressure and displacement
  longitudinal wave.
• The velocity of sound at 20 C and one atmosphere
  is 343 m/s.
• v 343 0.60( TC 20 C)

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Physics 1710Chapter 17 Sound

• 1' Lesson
• The pressure amplitude is ?Pmax ?v ? smax
• The intensity of a sound wave is the power
  divided by the area over which it is spread
  I P/ A ½ ? v (? smax) 2
• The Sound Intensity Level (SIL) ? is equal to
  ten times (10 x) the logarithm of the ratio of
  the intensity to the reference level of 1 pW/m 2
  
• 10 Log (I / I o )

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Physics 1710Chapter 17 Sound

• Summary
• I Pave/A Pave/(4? r 2)
• The Doppler Effect is a shift in the frequency
  of a source due to the relative motion of the
  source and observer.
• f ' (v vo )/(v vs) f