Question

A boy is walking away from a wall at a speed of 1m/s in a direction at right angle to the wall. As he walks, he blows a whistle steadily. An observer towards whom the boy is walking hears 4 beats per second. If the speed of sound is 340m/s, what is the frequency of the whistle?

• A. 680 Hz
• B. 720 Hz
• C. 760 Hz
• D. 800 Hz

Answer 1

The correct option is A 680 Hz

The situation is equivalent to two sources giving beats. First is the whistle of the boy and the second is wall.
$f_b=f_s-f_{s^{\prime }}$
$4=f\left(\frac{340}{340-1}\right)-f\left(\frac{340}{340+1}\right)$
Or $4=f(1-\frac{1}{340})-f(1+\frac{1}{340})$ on applying binomial approximation,
$4=f(1+\frac{1}{340})-f(1-\frac{1}{340})=\frac{f}{170}$ or $f=680Hz$