Question

what id doppler effect? derive the expression for apparent frequency when the source and the observer are moving towards each other

Answer 1

Answer:

The Apparent change in the frequency of sound when the source, the observer and the medium are in a relative motion is called Doppler Effect.

Let S be source of sound moving with velocity v

s

towards stationary listener O.

Distance travelled in time time period, T=v

s

T

Therefore apparent wavelength, λ

′

=λ−v

s

.T

If frequency is ν then,

λ=λ

′

−v

s

T

λ=λ

′

−

ν

v

s

=

ν

v−v

s

; v=νλ

If apparent frequency heard by listener is ν

′

ν

′

=

λ

′

v

=

v−v

s

νv

Thus apparent frequency is greater than the actual frequency as source moves towards listener.

Similarly if source moves away from listener.

ν

′

=

λ

′

v

=

v+v

s

νv