Question

The velocity of sound in any gas depends upon:

• A. The wavelength of sound only
• B. The intensity of sound waves only
• C. Density and elasticity of gas
• D. The amplitude and frequency of sound

Answer 1

The correct option is C

Density and elasticity of gas

The explanation for the correct option :

1. Sound is a mechanical wave. It requires a medium to propagate.
2. Sound travels through a medium by stretching and compressing it continually. This creates a disruption in the medium, which spreads. Sound flows across the medium in this manner.
3. As a result, the speed will be determined by certain of the medium's material features, which will either facilitate or obstruct this continual stretching and compressing operation.
4. These parameters are the bulk modulus of elasticity and the density of the gas, respectively, for gases. The elasticity of a gas and the ease with which it may be stretched and compressed are determined by its bulk modulus of density.
5. This continual stretching and compression are hampered by the density. As a result, according to the Newton Laplace equation,

$$\begin{gathered} v=\frac{K}{\rho } \\ wherevisthespeedofsoundinthegas \\ Kisthegas\text{'}sbulkmodulusofelasticity, \\ \rho isthegas\text{'}sdensity. \end{gathered}$$

6. Hence, As a result, the speed of sound in a gas is determined by its density and elasticity.

The explanation for the incorrect option,

In option A,

1. Since the velocity of the wave in a medium is constant.
2. When the wavelength rises, the frequency reduces by the same amount, resulting in a constant product. As a result, the wavelength is essentially determined by the wave's speed.
3. The wavelength, on the other hand, has no bearing on the wave's speed.

In option B,

The speed of sound depends on the medium and not on the intensity of the wave.

in option D,

1. The speed of sound is independent of frequency and amplitude.
2. When frequency changes, wavelength changes thus maintaining a constant speed.

Hence, the correct option is (C) Density and Elasticity of gas.