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.

Options

A. 205 m
B. 300 m
C. 180 m
D. 270 m

Answer

D

Explanation

For not hearing echo, the time interval between the beat of drum must be equal to time of echo
`t_(1)=(2d)/(v)=(60)/(40)=(3)/(2)implies2d=(3v)/(2)...(i)`
and `t_(2)=(2(d-90))/(v)=(60)/(60)=1`
`implies 2d-180=v...(ii)`
From (i) and (ii)
`implies (3v)/(2)-180=vimpliesv=360m//s`
Now, `(2d)/(360)=(3)/(2)impliesd=270m`.