Question

A boy is walking away from a wall at a speed of 1.0 m/s in a direction at right angles to the wall. The boy blows a whistle steadily. An observer towards whom the boy is moving hears 4 beats/s. If the speed of sound is 340 m/s, the frequency of whistle is

• A. 480 Hz
• B. 680 Hz
• C. 840 Hz
• D. 1000 Hz

Answer 1

The correct option is B 680 Hz

The frequency of direct sound of whistle heard by observer is
$n_1=\frac{v}{v-v_s}n=\frac{340}{340-1}\times n=\frac{340}{339}n$ (i)
Frequency of sound of whistle reflected by wall is
$n_2=\frac{v}{v+v_s}n=\frac{340}{341}n$ (ii)
Given, $n_1-n_2=4$
Therefore,$\frac{340}{339}n-\frac{340}{341}n=4$
$\Rightarrow n=680Hz$