The Doppler Effect

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The Doppler Effect
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Spherical and Plane Waves

• Sound emanates from a source in all directions at
  the same speed (assuming medium is constant
  everywhere), and therefore takes the shape of
  concentric spheres for the wave fronts.
• At large distances from the source these wave
  fronts can be regarded as plane waves.

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Spherical Wave
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Spherical into Plane Waves
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Doppler Effect

• Experienced whenever there is relative motion
  between a source of waves and an observer.

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What is happening at A and B?
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Relative Motion

• When source and observer are moving toward each
  other, observer hears a frequency higher than
  source frequency.
• When source and observer are moving away from
  each other, observer hears a lower frequency.

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Relative motion towards

• Frequency of car horn remains the same, the wave
  fronts reach an observer in front of the car more
  often than they would if the car were stationary.
• During motion towards each other, observer
  detects an additional number of wave fronts.

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Relative motion away

• The wave fronts reach the observer behind the car
  less often than they would if the source were
  stationary.
• When observer and source are traveling away from
  each other, fewer wave fronts are detected per
  second.

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Source Moving Toward Stationary Observer

• f f / (1 vs/v)
• f perceived frequency
• f actual frequency
• vs speed of source
• v speed of sound

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Source Moving Away from Stationary Observer

• f f / (1 vs/v)
• f perceived frequency
• f actual frequency
• vs speed of source
• v speed of sound

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Observer Moving Toward Stationary Source

• f f (1 vo/v)
• f perceived frequency
• f actual frequency
• vo speed of observer
• v speed of sound

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Observer Moving Away from Stationary Source

• f f (1 vo/v)
• f perceived frequency
• f actual frequency
• vo speed of observer
• v speed of sound

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If Both are Moving

• If they are moving toward each other
• f f (1 vo/v) / (1 vs/v)
• If they are moving away from each other
• f f (1 - vo/v) / (1 vs/v)

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Example Problem

• A train moving at a speed of 40.0 m/s sounds its
  whistle, which has a frequency of 500 Hz.
  (a) Determine the frequency heard by a stationary
  observer as the train approaches the observer.
  (b) as the train passes and is leaving the
  observer.

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Example Problem II

• An ambulance travels down a highway at a speed of
  40.0 m/s, its siren emitting sound at a frequency
  of 400 Hz. What frequency is heard by a
  passenger in a car traveling at 30.0 m/s in the
  opposite direction as the car (a) approaches? (b)
  moves away from the ambulance? (take the speed
  of sound to be 345 m/s)

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Example Problem III

• Find the speed of a police car racing down the
  road with his siren emitting a frequency of 400
  Hz if a stationary observer hears an observed
  frequency of 440 Hz. (take speed of sound to be
  345 m/s)

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Doppler Effect for Light
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Mach number

• What happens as the source speed approaches the
  speed of sound?
• What happens when the source speed becomes
  greater than the speed of sound?
• Ratio of source speed to sound wave speed is mach
  number.

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Sonic Boom!

• As source exceeds the wave velocity, a conical
  wave front is produced (shock wave)

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Shock Wave