(i) In a car race sound signals emitted by the two cars are detected by the detector on the straight track at the end point of the race. Frequency observed is 330 Hz and 360 Hz. The original frequency of horn is 300 Hz for both cars. Race ends with the separation of 1000 m between the cars. Assume both cars move with constant velocity and velocity of sound is 330 m/s. Find the time (in seconds) taken by the winning car to finish the race.
(ii) A source of sound of frequency f is dropped from rest from a height h above the ground. An observer `O_(1)` is located on the ground and another observer `O_(2)` is inside water at a depth d from the ground. Both `O_(1)` and `O_(2)` are vertically below the source. The velocity of sound in water is 4V and that in air is V. Find
(a) The frequency of the sound detected by `O_(1)` and `O_(2)` corresponding to the sound emitted the source initially.
(b) The frequency detected by both `O_(1)` and `O_(2)` corresponding to the sound emitted by the source at height `h//2` from the ground.

Answer

(i) 40 s
(ii) (a) `f_(2)=f_(1)=(2vf^(2))/(2vf-g)`
(b) `f_(1)=f_(2)=(2vf^(2))/(2(v-sqrt(gh))f-g)`