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A sound wave of frequency $640 Hz$ travels $800 m$ in $2.5 s$ . What is the speed and wavelength of the sound wave?

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220 m / s and 0.3 m

340 m / s and 0.5 m

360 m / s and 0.6 m

320 m / s and 0.5 m

answer is D.

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Detailed Solution

A sound wave of frequency

640 Hz

travels

800 m

2.5 s

. The speed and wavelength of the sound wave is

320 m / s and 0.5 m

respectively.
Given,
Frequency of wave,

f = 640 Hz

Distance through which the wave travels,

s = 800 m

Time taken,

t = 2.5 s

It is known that

speed of wave = \frac{Distance}{Time}

it can also be written as

\Rightarrow v = \frac{s}{t}

where

v

s

and

t

are the speed of the wave, distance and time.
on substituting the given values, we get

\Rightarrow v = \frac{800}{2.5}

\Rightarrow v = 320 m / s

Now, wavelength of wave is given as

λ = \frac{v}{f}

where,

λ

is the wavelength,

v

is the speed and

f

is the frequency of the wave.
on substituting the given values, we get

\Rightarrow λ = \frac{320}{640}

\Rightarrow λ = 0.5 m

Hence, the speed and wavelength of the sound wave are

320 m / s

and

0.5 m

respectively.

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