Doppler Effect

1
Doppler Effect

• When the object and the receiver are traveling at
  different speeds, the frequency changes
• Change depends on whether the object or the
  receiver is moving, or both
• Assume the original frequency is f0

2
Stationary Source, Moving Receiver

• Let receiver be to right of source, moving to the
  right at a speed of vR.
• Let sound leave source with speed v.

3

• Receiver sees wavefronts moving past at a speed
  of v v - vR. Thus

• If receiver is towards object, replace (-) with
  ()

4
Moving Source, Stationary Receiver

• Let receiver be to right of source and stationary
• Let source be moving to right with speed vS.
• Let sound leave source at speed v.

5

• Wavelength changes as object moves
• Apparent wavelength is

• Thus, ahead of object

6
Combined motion

• Treat as vectors, with positive to the right

7

• Two trains, both traveling north, pass through a
  station. The first train is moving at a speed of
  13.3 m/s, while the second has a speed of 8.89
  m/s. As it reaches the beginning of the platform,
  the second train blows its whistle. The first
  train is ahead of the second train, just clearing
  the end of the platform. If the whistle has a
  frequency of 450 Hz and the speed of sound is 345
  m/s, what frequency is heard by a) a passenger on
  the first train? b) a passenger on the second
  train? c) a passenger on the platform?

8
Supersonic motion

• When the object is traveling faster than the
  speed of sound, it is going supersonic
• Waves pile up, generating a sonic boom