Question

The propagation of a sound wave in a gas is given by the equation
$\frac{d^{2}y}{d{t}^2}=\frac{k}{l}.\frac{d^{2}y}{d{x}^2}$.
Then the velocity of sound is given by

• A. $\frac{k}{l}$
• B. $\frac{l}{k}$
• C. $\sqrt{\left(\frac{k}{l}\right)}$
• D. $\sqrt{\left(\frac{l}{k}\right)}$

Answer 1

The correct option is C $\sqrt{\left(\frac{k}{l}\right)}$

We know that

$\frac{d^{2}y}{d{t}^2}=\frac{k}{l}.\frac{d^{2}y}{d{x}^2}$
Comparing with the equation
$\frac{d^{2}y}{d{t}^2}={\nu }^2\frac{d^{2}y}{d{x}^2}$
${\nu }^2=\frac{k}{l}$
$\nu =\sqrt{\frac{k}{l}}.$