A man standing in front of a mountain beats a drum at regular intervals. The drumming rate is gradually increased and he finds that echo is not heard distinctly when the rate becomes `40` per minute. He then moves near to the mountain by `90` metres and finds that echo is again not heard distinctly when the drumming rate becomes `60` per minute. Calculate (a) the distance between the mountain and the initial position of the man and (b) the velocity of sound.

Explanation

Let d: initial distance between man and mountain.
Number of drumming beat `= 40` per min
`= (40)/(60)` per sec `= (2)/(3) s^(-1)`
Time interval between successive beats `= (3)/(2) s = 1.5`

`(2d)/(v) = 1.5` (i)

`(2(d - 90))/(v) = (1)/(60//60) = 1` (ii)
`(i)//(ii)`
`(d)/(d - 90) = 1.5 rArr d = 1.5d - 135`
`d = 270 m`
`v = (2d)/(1.5) = (4)/(3) xx 270 = 360 m//s`