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Sound - Doppler Effect

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The change in frequency of sound due to relative motion between a source and a listener is called the Doppler Effect.

The observed sound frequency for a listener can be expressed as

fr = fs (c + vr) / (c + vs)                                 (1)


fr = frequency observed by the receiver (1/s, Hz)

fs = frequency emitted from the source (1/s, Hz)

c = speed of sound (m/s) 

vr = velocity of the receiver relative to the medium - positive if the receiver is moving towards the source(m/s)

vs = velocity of the source relative to the medium - positive if the source is moving away from the receiver (m/s)

Example - A Train passing a Bell

A train with speed 200 km/h (55.6 m/s) passes a bell with sound frequency 1000 Hz. With an air temperature of 20 oC the speed of sound is 343 m/s.

The frequency observed by a passenger in the train before passing the bell can be calculated as

fr = (1000 Hz)((343 m/s) + (55.6 m/s)) / ((343 m/s) + (0 m/s))  

  = 1162 Hz

The frequency observed by the passenger in the train after passing the bell can be calculated as

fr = (1000 Hz) ((343 m/s) + (- 55.6 m/s)) / ((343 m/s) + (0 m/s))  

  = 838 Hz


Doppler Effect Calculator

Calculate the observed frequency with the calculator below:

Download and print the Doppler Effect Chart

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