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.
Derive general expressions for the spacing of the pies $\lambda$ and the frequency $f$ with which they are received by the pie eater in terms of the speed of the belt $v$, the speed of the sender $u_s$, the speed of the receiver $u_r$ and the frequency $f_0$ with which the piemaker places pies on the belt.

Answer 1

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

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

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

$\lambda =\frac{v}{f_o}=15m/s$

$f=f_o\left(\frac{v-v_r}{v-v_s}\right)$