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in Physics by (53.6k points)

A person standing in front of a mountain at a certain distance beats a drum at regular intervals. The drum¬ming rate is gradually increased, and he finds that the echo is not heard distinctly when the rate becomes 50 per minute. He then moves nearer to the mountain by 100 meters, and finds that the echo is again not heard when the drumming rates become 60 per minute. Calculate: 

1. The distance between the mountain and the initial position of the man, 

2. Velocity of sound.

1 Answer

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Best answer

Let ‘s’ be the distance between the man and the mountain and let ‘v’ be the velocity of sound.

Given 

: Drumming rate = 50 per minute. 

∴ Interval between successive beats

= \(\frac{60}{50}\) = 1.2/sec

Time taken by the echo = 2s/v

Given that when the drumming rate is 50 per minute, echo is not heard by the man 

⇒ beats overlap in time frame

i.e., 2s/v = 1.2 .........(2)

Similarly when the person moves 100 m towards the mountain, with drumming rate = 60 per minute

Substituting this in (1) we get. 

v = 1000 m/s

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