Two sources A and B are sounding notes of frequency 680 Hz. A listener moves fro

Question

Two sources A and B are sounding notes of frequency 680 Hz. A listener moves from A to B with a constant velocity u. If the speed of sound is 340 m/s, what must be the value of u so that he hears
10 beats per second?

Options:

A . 2.0 m/s

B . 2.5 m/s

C . 30 m/s

D . 3.5 m/s

Answer: Option B
:
B
Apparent frequency due to source A is

n^{'} = \frac{v - u}{v} \times n

Apparent frequency due to source B is

n "= \frac{v + u}{v} \times n

∴ n " - n^{'} = \frac{2 u}{v} \times n = 10

∴ u = \frac{10 v}{2 n} = \frac{10 \times 340}{2 \times 680} = 2.5 m / s

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