The Doppler Effect

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The Doppler Effect

• Section 14.6

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• The Doppler Effect A change in frequency (pitch)
  due to relative motion between a source of sound
  and its observer

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• The Doppler Effect can be produced by either the
  source moving or by the observer moving.

Doppler Effect for a Moving Observer
Actual Wave Observed Wave
Large wavelength Small frequency (low pitch )
Small wavelength Large frequency (high pitch)
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Moving Sound Source

• For a sound source moving towards a stationary
  observer with speed vs , the perceived wavelength
  decreases and velocity remains constant
• Therefore observed frequency will increase from f
  to f
• For a sound source moving away from a stationary
  observer with speed vs , the perceived wavelength
  increases and velocity remains constant
• Therefore observed frequency will decrease from f
  to f

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Moving Observer

• For an observer moving towards a stationary sound
  source with speed v0 , the perceived velocity
  increases and wavelength remains constant
• Therefore observed frequency will increase from f
  to f
• For an observer moving away from a stationary
  sound source with speed v0 , the perceived
  velocity decreases and wavelength remains
  constant
• Therefore observed frequency will decrease from f
  to f

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In general, the resulting frequency can be found
using the following formula

• Use the top set of signs ( in numerator - in
  denominator) when the objects are moving towards
  each other
• Use the bottom set of signs (- in numerator
  in denominator) when the objects are moving away
  from each other

(new) observed frequency
speed of observer
(old) actual frequency
speed of sound (usually 343 m/s)
speed of sound source
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• Some everyday examples are
• Radar detectors
• Waves that strike an approaching car will bound
  back with a higher frequency
• Waves that strike a car moving away will bounce
  back with a lower frequency

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• Loud fire engines/sirens moving past you
• As the fire engine/siren approaches, the pitch of
  the siren sound (a measure of the siren's
  frequency) is high
• As the fire engine/siren passes by, the pitch of
  the siren sound is low.
• Virtual Physic Lab Simulation

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• Animals (bats)
• A) Stationary object Waves will reflect off
  surface with same spacing as when they arrived
  no shift in frequency between cry and echo
• B) Insect flying away Echo waves will have wider
  spacing (lower frequency) than cry waves because
  insect moves farther from bat between waves
• C) Insect approaching Echo waves will be more
  compressed (higher frequency) than cry waves
  because insect moves closer to bat between waves

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Shock Waves and Sonic Booms

• How fast are the following aircrafts moving with
  respect to the speed of sound? (slower than, at,
  or faster than?)

Aircraft moving at the speed of sound
Aircraft moving faster than the speed of sound
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• What is the V shape that forms behind an
  aircraft traveling faster than the speed of
  sound?
• What causes the V shape?
• Compressions interfere (overlap)
• Superposition of compressions
• One BIG compression all at once

High pressure regions result from the overlapping
of compressions
What do you hear as the result of this big
compression?
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• When do you hear a sonic boom?
• As the high pressure region hits your ears all at
  once!
• NOT as a plane crosses the threshold of sound

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• Where else in the real world do you see the V
  shape occur?
• Water behind a duck
• Boats
• Wakeboarding/Waterskiing

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Video on Doppler and Sonic

• http//www.youtube.com/watch?vyWIMWqkcRDUfeature
  related