First slide

Introduction to waves

Question

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

Moderate

A

$\frac{v_{s}}{2}$
B

$\frac{v_{s}}{12}$
C

$12 v_{s}$
D

$\frac{3}{2} v_{s}^{2}$

Solution

$v_{sound} \propto \frac{1}{\sqrt{ρ}} \Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{ρ_{2}}{ρ_{1}}} = \sqrt{\frac{4}{1}} = 2 \Rightarrow v_{2} = \frac{v_{1}}{2} = \frac{v_{s}}{2}$

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