Question

If the speed of sound in gas in a beaker is thrice that of the speed of sound in gas in another beaker, what will be the ratio of densities of gases in beakers?

• A. $3:2$
• B. $2:3$
• C. $1:9$
• D. $9:1$

Answer 1

The correct option is C $1:9$

We know that the speed of sound is inversely proportional to the square root of density of medium, i.e.,
$v\propto \sqrt{\frac{1}{\rho }}$
So, as per the question, $v_2=3\times v_1$
And according to the proportionality we have,
$\frac{v_1}{v_2}=3=\sqrt{\frac{{\rho }_2}{{\rho }_1}}$
or $\frac{{\rho }_2}{{\rho }_1}=9$
But we have to determine the ratio of densities in first beaker to that in second beaker,
So, $\frac{{\rho }_1}{{\rho }_2}=\frac{1}{9}$