Question

The velocity of sound in any gas depends upon:
A. Wavelength of sound only
B. Density and elasticity of gas
C. Intensity of sound waves only
D. Amplitude of frequency of sound

Answer 1

Hint: Since, sound is a mechanical wave, its speed depends on some physical properties of the medium. Specifically if the medium is elastic it is better for faster propagation of sound and if it is too dense, the medium tries to slow it down.

Formula used:
$v=\sqrt{\dfrac{K}{\rho }}$
where $v$ is the speed of sound in the gas, $K$ is the bulk modulus of elasticity of the gas and $\rho $ is the density of the gas.

Complete step-by-step answer:
Sound is a mechanical wave. Hence, it depends upon the presence of a medium and its properties to propagate through it. Sound propagates through a medium by continuously stretching and compressing it. This causes a disturbance in the medium which propagates further. This is how sound travels through the medium.
Now the speed will therefore be dependent on some material properties of the medium that either ease or disrupt this continuous stretching and compressing process.
Specifically for gases, these properties are the bulk modulus of elasticity of the gas and the density of the gas. The bulk modulus of density determines the elasticity of the gas and the relative ease by which it can be stretched and compressed.
The density hinders this constant stretching and compression. Hence, by the Newton-laplace equation,
$v=\sqrt{\dfrac{K}{\rho }}$ --(Newton-Laplace equation) where $v$ is the speed of sound in the gas, $K$ is the bulk modulus of elasticity of the gas and $\rho $ is the density of the gas.
Hence, the speed of sound in a gas depends upon the density and the elasticity of the gas.
Therefore, the correct option is B) Density and elasticity of the gas.

Note: Students might have heard that the product of wavelength and frequency equals the speed of a wave and hence, may be tempted to mark option A) as the correct answer. However, this is completely wrong, since the speed of a wave remains constant in a medium. If the wavelength increases then the frequency decreases by an equal measure such that their product always remains constant. Hence, in essence, the wavelength depends on the speed of the wave. However, the speed of the wave does not depend on the wavelength.