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The Doppler Effect

Here is a quick guide to understanding the doppler effect, to help you do your physics homework or assignment:

For an observer moving at a speed v_o towards the source of a sound moving at v_s, the observed frequency of the sound is

f_o=f_s(\frac{v+v_o}{v-v_s})

where v=343 m/s is the speed of sound at 20o C.  v_o is positive when moving towards the source, and v_s is positive when moving towards the observer.

 

Examples

1.  Standing at a crosswalk, you hear a frequency of 560 Hz from the siren of an approaching ambulance.  After the ambulance passes, the observed frequency of the siren is 480 Hz.  Determine the ambulance's speed and the frequency of the source.

given,

v_o=0\,m/s

v=343 \, m/s

When the ambulance is approaching,

560=f_s(\frac{343}{343-v_s})

and when the ambulance is receding,

480=f_s(\frac{343}{343+v_s})

solving this system gives

 v_s=26.38\,m/s

 f_s=516.9\,Hz

 
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