# 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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Let d: initial distance between man and mountain.
Number of drumming beat = 40 per min
= (40)/(60) per sec = (2)/(3) s^(-1)
Time interval between successive beats = (3)/(2) s = 1.5 (2d)/(v) = 1.5 (i) (2(d - 90))/(v) = (1)/(60//60) = 1 (ii)
(i)//(ii)
(d)/(d - 90) = 1.5 rArr d = 1.5d - 135
d = 270 m
v = (2d)/(1.5) = (4)/(3) xx 270 = 360 m//s