# 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

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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.

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Correct Answer - 270 m
Time interval between beats (initially) = (60)/(40) = 1.5 sec
Since t = (2S)/(v)
1.5 = (2S)/(2v)
where S is the initial distance and v is the speed of sound . As the man approches 90m towards the mountain
(2(S - 90))/(v) = 1 since drumming rate is 60//min
Solving for S from the two relations we get
(2S)/(2(S - 90)) = 1.5 , (S - 90) /(S) = (2)/(3)
rArr 3S - 3 xx 90 = 2S , S = 270 m