A source of sound is moving towards a stationary observer with velocity ' V S ' and then moves away with velocity ' V S '. Assume that medium through which the sound waves trav

Question

A source of sound is moving towards a stationary observer with velocity ' V S ​ ' and then moves away with velocity ' V S ​ '. Assume that medium through which the sound waves travel is at rest. If 'V' is the velocity of sound and 'n' is the frequency emitted by the source then the difference between the apparent frequencies heard by the observer is

TestHub · Accepted Answer

Apparent frequency when the source moves towards the stationary observer is given by

$n_{1} = n (\frac{V}{V - V _{s}})$

Apparent frequency when the source moves away from the stationary observer is given by

$n_{2} = n (\frac{V}{V + V _{s}})$

The difference between the apparent frequencies is

$Δ n = n_{1} - n_{2}$

$Δ n = n (\frac{V}{V - V _{s}}) - n (\frac{V}{V + V _{s}})$

$Δ n = nV (\frac{1}{V - V _{s}} - \frac{1}{V + V _{s}})$

$Δ n = nV (\frac{V + V _{s} - ( V - V _{s} )}{V ^{2} - V _{s}^{2}})$

$Δ n = \frac{2 nV V _{s}}{V ^{2} - V _{s}^{2}}$

Answer: $\frac{2 nV V _{s}}{V ^{2} - V _{s}^{2}}$

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