Question

The speed of sound in a gas of density $\rho$ at a pressure $p$ is proportional to

• A. $\left(\frac{p}{{\rho }^2}\right)$
• B. ${\left(\frac{p}{\rho }\right)}^{\frac{3}{2}}$
• C. $\sqrt{\left(\frac{p}{\rho }\right)}$
• D. ${\left(\frac{\rho }{p}\right)}^2$

Answer 1

The correct option is C

$\sqrt{\left(\frac{p}{\rho }\right)}$

Step 1: Given Data:

Density of gas$=\rho$

Pressure of gas$=p$

Step 2: Formula Used:

The speed of sound in a gas,

$\left(v\right)=\sqrt{\frac{\gamma p}{\rho }}$

Where, $\gamma =$the ratio of specific heats, $p=$the pressure of the gas, $\rho =$density of the medium

Step 3: Calculating the speed of sound

We know that speed of sound$\left(v\right)=\sqrt{\frac{\gamma p}{\rho }}$

Therefore, the speed of sound in a gas $v\propto \sqrt{\frac{p}{\rho }}$

Hence option C is the correct answer.