Question

the speed of sound in oxygen at a certain temperature is 460m/s.the speed of sound in helium at same temperature will be

Answer 1

The speed of sound in oxygen (O2) at a certain temperature is 460 ms−1.

The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal) 1420 ms.

550 ms.

Answer 2

$v_h=1419.59\ m.s^{-1}$ is the speed of sound in helium at the same temperature.

Explanation:

Given:

• Speed of sound in oxygen, $v_o=460\ m.s^{-1}$

• Since oxygen is a diatomic gas and we have the adiabatic index, $\gamma_2=1.4$

• Since Helium is a mono-atomic gas and we have the adiabatic index,$\gamma_1=\frac{5}{3}$

For speed of sound in ideal gases we have the relation:

$v=\sqrt{\frac{\gamma.R.T}{M} }$ .............................(1)

Using the above eq. (1) for Oxygen:

$460=\sqrt{\frac{1.4\times 8.314\times T}{32\times 10^{-3}} }$

$T=581.74\ K$

Now for helium:

$v_h=\sqrt{\frac{\frac{5}{3}\times 8.314\times 581.73 }{4\times 10^{-3}} }$

$v_h=1419.59\ m.s^{-1}$

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TOPIC: speed of sound in gases

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