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in Physics by (61.3k points)

A band playing music at frequency f is moving toward a wall with velocity Vs. A motorist is following the band with a speed of Vm. If V is speed of sound, obtain an expression for the beat frequency heard by the motorist.

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In this case, both the source and the observer moving with different speeds towards the wall so the frequency of sound heard by motorist is given as

f' = f0 [v + vm/v + vs]

While the sound reflected from the wall is moving towards the motorist. Hence the frequency heard by

the motorist will be f''  = fw  [v + vm/v] . These two waves superimpose with each other to create beats and number of beats heard is given by n = f" - f' .

The frequency, f, of band heard by the motorist directly is given by  f' = f[v + vm/vs] .

The frequency fw reaching the wall is

The frequency f″ reaching the motorist is given by

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