A person in front of a mountain is beating a | vedclass

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(C) Since the drummer does not hear any echo,the time interval between two successive drum beats must be equal to the time taken by the sound to trave

Vedclass · Accepted Answer

$360$

Vedclass · Answer

(C) Since the drummer does not hear any echo,the time interval between two successive drum beats must be equal to the time taken by the sound to travel to the mountain and back.Let $x$ be the initial distance from the mountain and $v$ be the speed of sound.The time interval between two beats in the first case is $T_1 = \frac{60}{40} = 1.5 \, s$.The time taken for sound to travel to the mountain and back is $\frac{2x}{v}$.So,$\frac{2x}{v} = 1.5 \implies 2x = 1.5v \quad \dots(i)$In the second case,the distance becomes $(x - 90) \, m$ and the rate is $60$ beats per minute.The time interval between two beats is $T_2 = \frac{60}{60} = 1.0 \, s$.So,$\frac{2(x - 90)}{v} = 1.0 \implies 2x - 180 = v \quad \dots(ii)$Substituting $2x = 1.5v$ from equation $(i)$ into equation $(ii)$:$1.5v - 180 = v$$0.5v = 180$$v = \frac{180}{0.5} = 360 \, ms^{-1}$.

$A$ person in front of a mountain is beating a drum at the rate of $40$ per minute and hears no distinct echo. If the person moves $90 \, m$ closer to the mountain,he has to beat the drum at $60$ per minute to not hear any distinct echo. The speed of sound is .............. $ms^{-1}$.

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