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A source is producing $15 oscillations$ in $3 seconds .$ The distance between a crest and the adjacent trough is $10 cm$ . Find the velocity of the wave?

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1 cm / \sec

1.5 cm / \sec

1 m / \sec

2 cm / \sec

answer is C.

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Detailed Solution

A source is producing

15 oscillations

3 seconds .

The distance between a crest and the adjacent trough is

10 cm

. The velocity of the wave is

1 m / \sec

.
According to the question, the source is producing

15

waves in every

3 seconds

,
The number of oscillations produced in one second is the frequency.
Therefore,

frequency (f) = 15 / 3 .

= 5 Hz

The distance between consecutive crest and trough is

10 cm

.
Therefore,

λ / 2 = 10

and

λ = 20 cm

From the relation between frequency, wavelength and wave velocity is

v = f \times λ

Thus, velocity

v = 5 \times 20

\Rightarrow v = 100 cm / \sec

\Rightarrow v

= 1 m / \sec

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