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If the period of small ripples on the water is $0.1 s$ and their wavelength is $5 cm$ , what is the speed of the waves?

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20 cm / s

50 cm / s

40 cm / s

45 cm / s

answer is B.

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Detailed Solution

If the period of small ripples on water is

0.1 s

and their wavelength is

5 cm

, the speed of the waves is

50 cm / s .

Given,
Period of small water ripples,

T = 0.1 s

Wavelength of ripples,

λ = 5 cm

In SI unit, the wavelength can be written as

λ = 0.05 m

It is known that the frequency

(f)

of a wave is inversely proportional to the time period

(T)

of the wave. Mathematically,

f = \frac{1}{T}

On substituting the given values, we get

\Rightarrow f = \frac{1}{0.1}

\Rightarrow f = 10 Hz

Now, it is known that

Speed of the wave = Frequency \times wavelength

It can also be written as

\Rightarrow v = f \times λ

where

v

f

and

λ

are the speed, frequency and wavelength of the wave.
On substituting the given values, we get

\Rightarrow v = 10 \times 0.05

\Rightarrow v = 0.5 m / s

\Rightarrow v = 50 cm / s

Hence, the speed of the wave is

50 cm / s

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