Q. The velocity of sound is $v_{s}$ in air. If the density of air is increased to 4 times, then the new velocity of sound will be
A) $\frac{v_{s}}{2}$
B) $\frac{v_{s}}{12}$
C) $12v_{s}$
D) $\frac{3}{2}v_{s}^{2}$
Explanation
(a) $v_{sound} \propto \frac{1}{\sqrt{\rho}} \Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{\rho_{2}}{\rho_{1}}} = \sqrt{\frac{4}{1}} = 2 \Rightarrow v_{2} = \frac{v_{1}}{2} = \frac{v_{s}}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.