Question

A man standing in front of a mountain beats a drum at regular intervals. The rate of drumming is increased and he finds that the echo is not heard distinctly when the rate becomes $40$ per minutes. He then moves nearer to the mountain by $90$ metres and finds that echo is again not heard when the drumming rate becomes $60$ per minutes. The distance between the mountain and the initial position of man is:

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

Answer 1

The correct option is D $270m$

let the initial distance between the man and the mountain is $x$

Time to hear the echo= $\frac{2x}{v}$

Beat frequency= 40per minute=40/60 per second= 2/3 per second

Time interval between two beats= 3/2 s

To hear the beats distinctly $\frac{2x}{v}=\frac{3}{2}$ ...(1)_

When the person moves towards the mountain by 90m then the time taken by sound is $\frac{2(x-90)}{v}$

Beat frequency=60per minute=1 per second

$\frac{(2x-90)}{v}=1$ ...(2)

Solving equation 1 and 2 we get

$x=270m$