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

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

Answer 1

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

$V=\sqrt{\frac{\gamma p}{\varrho }}$

$so,V\alpha \frac{1}{\sqrt{\varrho }}$

$so,\frac{v_1}{v_2}=\frac{1/\sqrt{{\varrho }_1}}{1/\sqrt{{\varrho }_2}}$

$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{{\varrho }_2}{{\varrho }_1}}$

$\Rightarrow \frac{{\vartheta }_s}{v_2}=\sqrt{\frac{2\varrho }{\varrho }}$

$\Rightarrow v_2=\frac{{\vartheta }_s}{\sqrt{2}}$