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?

• A. 2.0 m/s
• B. 2.5 m/s
• C. 30 m/s
• D. 3.5 m/s

Answer 1

The correct option is B 2.5 m/s

Apparent frequency due to source A is
$n^{\prime }=\frac{v-u}{v}\times n$
Apparent frequency due to source B is
$n"=\frac{v+u}{v}\times n$
$\therefore n"-n^{\prime }=\frac{2u}{v}\times n=10$
$\therefore u=\frac{10v}{2n}=\frac{10\times 340}{2\times 680}=2.5m/s$