A person in front of a mountain is beating a drum at the rate of … - Vidyadip

MCQ

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 .............. $ms^{-1}$

A
$320$
B
$340$
✓
$360$
D
$380$

✓

Answer

Correct option: C.

$360$

c
(c)

As drummer does not hear any echo this means time between two successive wavefronts is equal to time in which a wavefront reaches back to drummer.

Distance covered by sound $=2 x$

If $v=$ speed of sound, then

$\frac{2 x}{v}=$ time interval between two successive wavefronts.

So, we have

In case I, $\frac{2 x}{v}=\frac{60}{40} \quad \dots(i)$

In case II, $\frac{2(x-90)}{v}=\frac{60}{60} \quad \dots(ii)$

Substituting for $x$ from Eq. $(i)$ in Eq. $(ii)$, we get

$2 x-180=v$

$\Rightarrow \frac{3}{2}-180=v$

$\Rightarrow v=360 \,ms ^{-1}$

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