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

Suppose the car is going towards the wal at a speed u. The wall is statioN/Ary with respect to the air and the horn is going towards it. If the frequency of the horn is v, that received by the wall is
`v'=v/(v-u)v`.
the wall reflects this sound without changing the frequency. Thus, the wall becomes the source of frequency v and the car driver is the listener. The wall (which acts as the source now) is at rest with respect to the air and the car (which is the observer now) is going towards the wall al speed u. The frequency heard by the car-driver for this reflected wave is therefore,
`v''=(v+u)/v v'`
`=(v+u)/v.v/(v-u)v`
`=(v+u)/(v-u)v.`
Putting the values
`480=(v+u)/(v-u) 440`
or, `(v+u)/(v-u)=48/44`
`u/v=4/92`
`=or, u=4/92xx330ms^-1=14.3ms^-1=52kmh^-1`