Question

The velocity of sound is $V_s$ in air . If the density of air is increased to 4 times , the new velocity of sound is

• A. $\frac{V_s}{2}$
• B. $\frac{V_s}{12}$
• C. $12V_s$
• D. $\frac{3}{2}{V}_s^2$

Answer 1

The correct option is A $\frac{V_s}{2}$

$V_S=\sqrt{\frac{{\gamma }_{air}p}{{\rho }_1}}$

$V_S^{\prime }=\sqrt{\frac{{\gamma }_{air}p}{{\rho }_2}}$

$\frac{V_S^{\prime }}{V_S}=\sqrt{\frac{{\rho }_1}{{\rho }_2}}=\sqrt{\frac{{\rho }_1}{4\times {\rho }_1}}=\frac{1}{2}$

$V_S^{\prime }=V_S/2$

Option 'A' is correct.