The driver of a car approaching a vertical wall notices that the frequency of horn of his car changes from…
The driver of a car approaching a vertical wall notices that the frequency of horn of his car changes from 400 Hz to 480 Hz, when it gets reflected from the wall. Find the speed of car if that of sound is 330 m/s.
Solution
Sol. Let u be the speed of car towards the wall.
(a) Frequency received at wall The car is acting as source emitting frequency f and wall as stationary source.
vs = u vo = 0
f' = f\left(\frac{v - v$_{o}$}{v - v$_{s}$}\right) = f\left(\frac{v}{v + u}\right)
(b) Frequency received by driver Now, wall will act as a source, emitting frequency f' and driver as observer.
vo = u vs = 0
f'' = f'\left(\frac{v + v$_{o}$}{v - v$_{s}$}\right) = f\left(\frac{v}{v - u}\right)\left(\frac{v + u}{v}\right)
f'' = f\left(\frac{v + u}{v - u}\right)
480 = 400 \left(\frac{330 + u}{330 - u}\right)
1.2(330 - u ) = 330 + u
⇒ 2.2u = 66 ⇒ u = 30m/s
Answer: $u = 30m/s$