Question

The speed of sound in air undergoing adiabatic changes is given by, where \(\rho\) is the density of medium and \(E_s\) is adiabatic elasticity:

• A. \(v=\sqrt{\dfrac{\rho}{E_s}}\)
• B. \(v=\sqrt{E_s\rho}\)
• C. \(v=\sqrt{\dfrac{E_s}{\rho}}\)
• D. \(v=\dfrac{1}{\sqrt{E_s\rho}}\)

Hint:

Speed of sound is directly proportional to the square root of elasticity and inversely proportional to the square root of density.

Answer 1

The Correct Option is C

Concept:
The speed of sound in an elastic medium depends on the elastic property of the medium and its density. \[ v=\sqrt{\frac{\text{Elastic modulus}}{\text{Density}}} \]

Step 1: Identify the elastic modulus.
For sound waves in air undergoing adiabatic changes, the elastic modulus is adiabatic elasticity. \[ \text{Elastic modulus}=E_s \]

Step 2: Identify density.
Density of the medium is given as: \[ \rho \]

Step 3: Apply the formula. \[ v=\sqrt{\frac{E_s}{\rho}} \] \[ \therefore \text{Correct Answer is (C)} \]