Question

A sound source, fixed at the origin, is continuously emitting sound at a frequency of 660 Hz. The sound travels in air at a speed of $330m{s}^{-1}$. A listener is moving along the line x = 336 m at a constant speed of $26m{s}^{-1}$. Find the frequency of the sound as observed by the listener when he is (a) at y = -140 m, (b) at y = 0 and (c) at y = 140 m.

Answer 1

Frequency at y =140 m is, $n=\frac{v+v_0}{v-v_s}{n}_0$

$=\frac{330+26\times \frac{140}{364}}{330}\times 660$

$=340\times 2=680Hz$

(b)When y=0, velocity of observer with respect to source is zero.

So, required frequency =660 Hz

(c)When, y=140 m

$n=\frac{v-v_0}{v}\times 660$

$=\frac{330-\frac{26\times 140}{364}}{330}\times 660$

$=\frac{330-10}{330}\times 660=640Hz$