First slide

Doppler

Question

The apparent frequency of a note, when a listener moves towards a stationary source, with velocity of 40 m/s is 200Hz. 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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