MCQ
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
- ✓$\frac{{{v_s}}}{2}$
- B$\frac{{{v_s}}}{{12}}$
- C$12{v_s}$
- D$\frac{3}{2}v_s^2$
✓
Answer
Correct option: A.
$\frac{{{v_s}}}{2}$
a
${v_{sound}} \propto \frac{1}{{\sqrt \rho }} $
${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}$
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