Question

Hydrogen gas is filled in two identical bottles, $A$ and $B$, at the same temperature. The mass of hydrogen in the two bottles is $12$ gm and $48$ gm respectively. In which bottle will sound travel faster? How many times as fast as the other?

Answer 1

Given:

Mass of hydrogen in bottle $A=$ $w_1=12g$

Mass of hydrogen in bottle $B=$ $w_2=48g$

$\because$ Density $\propto$ Mass

$\frac{{\rho }_1}{{\rho }_2}=\frac{w_1}{w_2}$ and for velocity $V\propto \frac{1}{\sqrt{\rho }}\propto \frac{1}{\sqrt{w}}$

$\therefore V_1/V_2=\sqrt{{\rho }_2/{\rho }_1}=\sqrt{w_2/w_1}=\sqrt{\frac{48}{12}}=\sqrt{\frac{4}{1}}=\frac{2}{1}$

Hence sound will travel faster in bottle $A$ and speed will be twice as that of bottle $B$.