Question

A conveyor belt moves to the right will a speed $v=300m/min$. A very fast piemaker puts pies on the belt at a rate of $20$ per minute, and they are received at the other end by a pie eater.
The piemaker now walks with a speed of $30m/min$ toward the receiver while continuing to a put pies on the belt at $20$ per minute. Find the spacing of the pies and the frequency with which they are received by the stationary pie eater.

Answer 1

We have to use the concept of Doppler's effect here

$v=\frac{300m}{60s}=5m/s$

$f=\frac{20}{60}=\frac{1}{3}/sec$

$v_o=\frac{30}{60}=0.5m/s$ , $v_s=0$

$f^{\prime }=f\left(\frac{v+v_o}{v-v_s}\right)=\frac{1}{3}\left(\frac{5+0.5}{5}\right)$

$f^{\prime }=\frac{11}{30}Hz$

$Spacing=5\times \frac{30}{11}=13.6m$