Question

The velocity of sound is $v_s$ in air. If density of air is increased twice then the new velocity of sound will be :
(Assume isobaric condition)

• A. $v_s$
• B. $\frac{v_s}{\sqrt{2}}$
• C. $\sqrt{2}{v}_s$
• D. $\frac{3}{2}{v}_s$

Answer 1

The correct option is B $\frac{v_s}{\sqrt{2}}$

$v=\sqrt{\frac{\gamma P}{\rho }}$ , that is, $\frac{v_s^{\prime }}{v_s}=\sqrt{\frac{\rho }{2\rho }}\Rightarrow$ $v_s^{\prime }=\frac{v_s}{\sqrt{2}}$