The wavelength of a sound wave is 40 cm and the time period, T = 0.0005 s. How many seconds will it take to travel 4 km?

5 s

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11 s

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7 s

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16 s

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Solution

The correct option is A 5 s
Given:
Wavelength of the sound, $λ = 40 c m = 0.4 m$
Time period, $T = 0.0005 s$
Distance covered, $s = 4 k m = 4000 m$

Speed of the sound wave is given by:
$v = f λ$

But frequency is inverse of the time period.
$f = \frac{1}{T}$

$⟹ v = \frac{λ}{T}$
$v = \frac{0.4 m}{0.0005 s}$
$v = 800 m / s$

Using formula for speed, time taken to cover 4 km will be:
$t = \frac{s}{v}$
$t = \frac{4000 m}{800 m / s}$
$t = 5 s$

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