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[38]
A source produces $15$ waves in $3$ seconds. The distance between crest and trough is $15 cm$ . What will be the $velocity (V), wavelength (λ) and the frequency of the wave (v) ?$

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ν = 5 Hz; λ = 0.3 m; V = 1.5 m / s

ν = 7 Hz; λ = 0.5 m; V = 2.5 m / s

ν = 5 Hz; λ = 0.4 m; V = 1.0 m / s

ν = 8 Hz; λ = 0.5 m; V = 2 m / s

answer is A.

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Detailed Solution

A source produces

15

waves in

3

seconds. The distance between crest and trough is

15 cm

. Then

ν = 5 Hz, λ = 0.3 m, V = 1.5 m / s

.
Where

V = velocity of wave   λ = wavelength   v = frequency

Given a source produces

15

waves in

3

seconds
Then the number of waves produced in

1 second = \frac{15}{3}

1 second

= 5

Frequency is the number of waves produced in one second,

ν = 5 Hz

Given distance between crest and trough

= 15 cm

We know that wave length is twice the distance between crest and trough.

\Rightarrow λ = 2 \times 15 cm

\Rightarrow

= 30 cm

\Rightarrow

= 0.3 m

To calculate the velocity of wave with frequency

5 Hz

and having wavelength

λ = 0.3 m

\Rightarrow V = λν

\Rightarrow V = 5 Hz \times 0.3 m

\Rightarrow V = 1.5 m / s .

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