Question

A boy is walking away from a well at a speed of 1.0 m/s in a direction at right angles to the wall. As he walks, he blows a whistle steadily. An observer towards whom the boy is walking hears 4.0 beats per second. If the speed of sound is 340 m/s, what is the frequency of the whistle(in Hz)?

Answer 1

Frequency heard by observer directly from source

$f^{\prime }=f\left(\frac{v-0}{v-1}\right)$

Frequency heard by observer after reflection from wall

$f^{\prime \prime }=f\left(\frac{v-0}{v+1}\right)$ So,

$f^{\prime }-f^{\prime \prime }=4$

$(\frac{v}{v-1}-\frac{v}{v+1}=4)$ at $v=340$

$f=680Hz$