Question

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

(b) The velocity of sound are:

• A. $360m,270m/s$
• B. $270m,360m/s$
• C. $72m,360m/s$
• D. $150m,360m/s$

Answer 1

The correct option is B $270m,360m/s$

Suppose the velocity of sound is $V$ and the distance between the mountain and the initial position of the man is $d$.
First the drum beat was $40/minute$.

So, in a minute the distance traveled by sound is: $2d\times 40=V\times 60$.
Using same logic in second case:
$2(d-x)\times 60=V\times 60$. [where $=x=90m$]
Solving these two equation, we can get:
$d=270m$ & $V=360m/s$