Question

The velocity of sound in Hydrogen at $0^{\circ }C$ is $1248m/s$. What will be velocity of sound in mixture of two parts by volume of Hydrogen to one part of Oxygen? (Oxygen $16$ is times heavier than Hydrogen nearly).

• A. $725m/s$
• B. $653m/s$
• C. $510m/s$
• D. $430m/s$

Answer 1

Answer: (C)

$510m/s$

The velocity of sound in a medium inversely varies with the square root of the density of the medium, that is

$v\propto \frac{1}{\sqrt{\rho }}$

Also, Density of hydrogen = ${\rho }_H=2$

Density of oxygen = ${\rho }_O=32$

The the ratio of H: O in the mixture is $2:1$.

Density of the hydrogen and oxygen mixture

$={\rho }_{mix}=\frac{\left(2\right)\left(2\right)+\left(1\right)\left(32\right)}{2+1}$

$=\frac{36}{3}$

$=12$

$v_{H}at{0}^{\circ }=1248m{s}^{-1}$

thus $v_{mix}=?$

Applying the following equation,

$v_{mix}=v_H\sqrt{\frac{{\rho }_H}{{\rho }_{mix}}}$

$⟹v_{mix}=v_H\sqrt{\frac{2}{12}}$

$=v_H\times \sqrt{.1667}$

$=1248\times 0.40829$

$\simeq 510m/s$

Option C is correct.