A racing car movnig towards a cliff, sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If v is the velocity of sound, then the velocity of the car is

Options

A. `v//2`
B. `v//sqrt(2)`
C. `v//4`
D. `v//3`

Answer

D

Explanation

Here, the frequency of the reflected sound as heard by the driver is twice the actual frequency of the sound of the horn because apparent pitch and hence frequency (since pitch `prop` frequency) is one octave higher than the actual one.
Now, we have, for the motion of the source, the
apparent frequecy, `n_(1)=n*(v)/(v-v_(c))`
where v is the velocity of sound and `v_(c)` is the velocity of the car.
Also, after reflection from the cliff, the directions of motions of the observer, i.e. the driver and of the sound become oppsite, for which there will be further modification of frequency.
The changed frequency is given by
`n_(2)=n_(1)*(v+v_(c))/(v)=n*(v)/(v-v_(c))*(v+v_(c))/(v)=n*(v+v_(c))/(v-v_(c))`
Now, by problem, `n_(2)=2n`.
`thereforen*(v+v_(c))?(v-v_(c))=2n implies v_(c)=(v)/(3)`.