First slide

Doppler's effect

Question

The apparent frequency of a note, when a listener moves towards a stationary source, with velocity of 40 m/s is 200 Hz. When he moves away from the same source with the same speed, the apparent frequency of the same note is 160 Hz. The velocity of sound in air is (in m/s)

Moderate

A

360
B

330
C

320
D

340

Solution

When a listener moves towards a stationary source apparent frequency
$n^{'} = (\frac{v + v_{0}}{v}) n = 200$ …..(i)
When listener moves away from the same source
$n^{''} = \frac{(v - v_{0})}{v} n = 160$ …..(ii)
From (i) and (ii)
$\frac{v + v_{0}}{v - v_{0}} = \frac{200}{160} \Rightarrow \frac{v + v_{0}}{v - v_{0}} = \frac{5}{4} \Rightarrow v = 360 m / \sec$

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