The driver of as car approaching a vertical wall notices that the frequency of his car's horn charges from 440 Hz to 480 Hz when it gets reflected from the wal. Find the speed of the car if that of the sound is `330 ms^-1`.

Explanation

Let `u` be 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
`{:(rarr v_(s)=u,,rarr v_(o)=0),(overset(*)(S),,overset(*)(O)),(,rarrv,):}`
`f' = f((v - v_(0))/(v - v_(s))) = f((v)/(v - u))`
(b) Frequency received by driver: Now wall will act as a source, emitting frequency `f'` and driver as observer
`{:(rarr v_(o)=u,,rarr v_(s)=0),(overset(*)(O),,overset(*)(S)),(,overset(v)larr,):}`
`f'' = f'((v + v_(0))/(v - v_(s))) = f((v)/(v - u)) ((v + u)/(v))`
`f" = f((v + u)/(v - u))`
`480 = 440((330 + u)/(330 - u))`
`1.2(330 - u) = 330 + u`
`2.2 u = 66 rArr u = 30 m//s`
Frequency of reflected sound:
(a) When car is moving towards wall

`f_(r) = f((v + u)/(v - u))`
(b) When car is moving away from wall

`f_(r) = f((v - u)/(v + u))`