The distance between a rarefaction and the next compression in a wave is $10 c m$ . The time period of the wave is $0.001 s$ . How much time will it take for the wave to travel a distance of $4 k m$ ?

5 s

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10 s

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20 s

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40 s

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Solution

The correct option is C $20 s$
The distance between a rarefaction and the next compression is $10 c m$ i.e $\frac{λ}{2} = 10 c m$
Hence,
$λ = 20 c m$ = $0.2 m$
The time period of the wave,
$T = 0.001 s$
The distance to be travelled,
$s = 4 k m$ = $4000 m$ .
We know that, speed of sound, $v = \frac{λ}{T}$
Thus, $v = \frac{0.2 m}{0.001 s}$

$\Rightarrow v = 200 m s^{- 1}$

The time taken by the wave to travel a distance of $4000 m$ ,
$t = \frac{D i s t a n c e}{S p e e d}$
$\Rightarrow t = \frac{4000 m}{200 m s^{- 1}} = 20 s$

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