Physics 110 Lecture 34 from Chapter 14 Sections 6 to 7

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Physics 110 Lecture 34 from Chapter 14
Sections 6 to 7

• Doppler Effect
• and Shock Waves

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Homework Assignment 34

• Problems
• Chapter 14, Problem 20 on page 492
• Chapter 14, Problem 28 on page 492
• Chapter 14, Problem 31 on page 493
• Chapter 14, Problem 68 on page 495

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Representations of Waves

• Wave fronts are the concentric arcs
• The distance between successive wave fronts is
  the wavelength
• Rays are the radial lines pointing out from the
  source and perpendicular to the wave fronts

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A Moving Sound Source.

• What happened to the spherical distribution of
  the waves when a source moves within a medium?

B
v
A
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Doppler Effect

• A Doppler effect is experienced whenever there is
  relative motion between a source of waves and an
  observer.
• When the source and the observer are moving
  toward each other, the observer hears a higher
  frequency
• When the source and the observer are moving away
  from each other, the observer hears a lower
  frequency

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Doppler Effect, cont.

• Although the Doppler Effect is commonly
  experienced with sound waves, it is a phenomena
  common to all waves
• Assumptions
• The air is stationary
• All speed measurements are made relative to the
  stationary medium

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Doppler Effect, Case 1 (Observer Toward Source)

• An observer is moving toward a stationary source
• Due to his movement, the observer detects an
  additional number of wave fronts
• The frequency heard is increased

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Doppler Effect, Case 1(Observer Away from Source)

• An observer is moving away from a stationary
  source
• The observer detects fewer wave fronts per second
• The frequency appears lower

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Doppler EffectCase 1 Equation

• Moving ObserverStationary Source
• When moving toward the stationary source, the
  observed frequency is
• When moving away from the stationary source,
  substitute vo for vo in the above equation

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Doppler Effect,Case 2 (Source in Motion)
Stationary ObserverMoving Source

• As the source moves toward the observer (A), the
  wavelength appears shorter and the frequency
  increases
• As the source moves away from the observer (B),
  the wavelength appears longer and the frequency
  appears to be lower

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Doppler Effect, Source Moving Equation

• Use vs when the source is moving toward the
  observer and -vs when the source is moving away
  from the observer

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Doppler Effect, General Case

• Both the source and the observer could be moving
• Use positive values of vo and vs if the motion is
  toward
• Frequency appears higher
• Use negative values of vo and vs if the motion is
  away
• Frequency appears lower

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Example 1

• A train passes a passenger platform at a speed of
  40 m/s. The horn sounds at 320 Hz.
• a) What frequency is heard by a person on the
  platform as the train approaches?
• b) What frequency is heard by a person on the
  platform as the train recedes?

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Example 1

• a) What frequency is heard by a person on the
  platform as the train approaches?
• Case of Moving Source--Stationary Observer.
• where fs 320 Hz v vsound 340
  m/s vo 0 vs 40
  towards

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Example 1

• b) What frequency is heard by a person on the
  platform as the train recedes?
• Case of Moving Source--Stationary Observer.
• where fs 320 Hz v vsound 340
  m/s vo 0 vs -40 m/s
  away

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Shock Waves

• A shock wave results when the source velocity
  exceeds the speed of the wave itself
• The circles represent the wave fronts emitted by
  the source

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Shock Waves, cont

• Tangent lines are drawn from Sn to the wave front
  centered on So
• The angle between one of these tangent lines and
  the direction of travel is given by sin ? v /
  vs
• The ratio v/vs is called the Mach Number
• The conical wave front is the shock wave

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Shock Waves, final

• Shock waves carry energy concentrated on the
  surface of the cone, with correspondingly great
  pressure variations
• A jet produces a shock wave seen as a fog