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A source of sound produces waves of wavelength $0.80 m$ in air. The same source of sound produces waves of wavelength $4.0 m$ in water. Suppose the velocity of sound in air is $332 m / \sec .$ The velocity of sound in water is given by which of the following?

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1568 m / \sec

1500 m / \sec

1660 m / \sec

1668 m / \sec

answer is C.

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Detailed Solution

A source of sound produces waves of wavelength

0.80 m

in air. The same source of sound produces waves of wavelength

4.0 m

in water. If the velocity of sound in air is

332 m / \sec .

The velocity of sound in water is

1660 m / \sec .

According to the question, wavelength (

λ)

of sound waves produced in air

= 0.80 m

The velocity of sound in air

(v) = 332 m / \sec .

From the relation between frequency, wavelength and wave velocity is

v = f \times λ

Therefore,

frequency (f) = v / λ

\Rightarrow f = 332 / 0.80

\Rightarrow frequency (f) = 415 Hz

It is given that; the same source of sound produces waves of wavelength

4.0 m

in the water.
Again, from the relation between frequency, wavelength and wave velocity is

v = f \times λ,

we can calculate the speed of sound in water.
Therefore,

velocity in water = 415 \times 4

= 1660 m / \sec

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