First slide

Doppler

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 1 0 beats per second ?

Moderate

A

2.0 m/s
B

2.5 m/s
C

3.0 m/s
D

3.5 m/s

Solution

Apparent frequency due to source A
$n^{'} = (\frac{V - V_{s}}{V}) n = (\frac{V - u}{V}) n Apparent frequency due to B n^{''} = (\frac{V + u}{V}) n n^{''} - n^{'} = 10 = (\frac{2 u}{v}) n or n = \frac{10 V}{2 n} = \frac{10 \times 340}{2 \times 680} = 2 \cdot 5 m / s$

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