Question

Select the correct relations between the velocity (v) of sound in a medium with the density (ρ) and the temperature of the gaseous medium.

• A. $\text{V}\propto \frac{1}{\rho }$
• B. $\text{V}\propto \frac{1}{\sqrt{\rho }}$
• C. $V\propto \sqrt{T}$
• D. $\text{V}\propto \frac{1}{{\text{T}}^2}$

Answer 1

Answer: (B), (C)

The correct options are
B $\text{V}\propto \frac{1}{\sqrt{\rho }}$
C $V\propto \sqrt{T}$

The velocity of sound in a gas is inversely proportional to the square root of the density of the gas. Hence, the velocity decreases as the density of the gas increases.

$\text{V}\propto \frac{1}{\sqrt{\rho }}$

The velocity of sound in a gas is directly proportional to the square root of its temperature. The velocity of sound in a gas increases with the increase in temperature.

$\text{V}\propto \sqrt{\text{T}}$