$40$ waves pass through a point in $0.5 s$ at $0^{o} C$ . The distance between one compression and adjacent rarefaction is $8 m$ . Find the velocity of the sound wave at $2457 K$ .

Open in App

Solution

If $40$ waves pass through a point in $0.5 s$ then it means one wave takes $\frac{0.5}{40} s e c$
This means that the time period 'T' is $\frac{0.5}{40} s e c$
The distance between one compression and adjacent rarefaction is half of wavelength. So wavelength $λ = 16 m$
We know that $s p e e d = \frac{λ}{T}$
Thus the speed at $0^{0} C e l c i u s = v_{1} = 16 \div \frac{0.5}{40} = \frac{16 \times 40}{0.5} = 1280$ m/s
From the given conditions we have $T_{1} = 0^{0} C e l c i u s = 273^{0} K e l v i n$ and $T_{2} = 2457 K$
We know that $\frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{2457}{273}} = 3$
Hence $v_{2} = v_{1} \times 3 = 1280 \times 3 = 3840$ m/s
The velocity of the sound wave at $2457 K$ is $3840 m / s$

Suggest Corrections

Similar questions

Q. A source is producing 1500 waves in 3 seconds. If the distance covered by a compression and an adjacent rarefaction be 68 cm, find: (a) frequency, (b) wavelength, and (c) velocity, of the sound wave.

Q. Distance between successive compression and rarefaction in a sound wave is

1 m

. If the velocity of sound is

360 {ms}^{- 1}

, find the frequency of sound wave.

A source producing 1500 sound waves in 3s. If the distance covered by a compression and an adjacent rarefaction be 68 cm. find a frequency, wavelength & velocity of sound waves

Ans 500hz, 1.36m and 680m/s

Pls solve fast

Q. A sound wave is passing through air column in the form of compression and rarefaction. In consecutive compression and rarefaction:

Q. A sound wave has a wavelength of 3 m. The distance from a compression centre to the adjacent rarefaction centre is?

Join BYJU'S Learning Program

40 waves pass through a point in 0.5s at 0oC. The distance between one compression and adjacent rarefaction is 8m. Find the velocity of the sound wave at 2457K.

$40$ waves pass through a point in $0.5 s$ at $0^{o} C$ . The distance between one compression and adjacent rarefaction is $8 m$ . Find the velocity of the sound wave at $2457 K$ .