Question

Velocity of sound in hydrogen at NTP is v. What will be the velocity of sound in a mixture of hydrogen and oxygen in the ratio 4 : 1 at NTP is .

• A. v
• B. 2v
• C. v/2
• D. v/4

Answer 1

Answer: (C)

v/2

Given:

Velocity of sound in hydrogen at N.T.P is v

A mixture of hydrogen and oxygen is in the ratio, 4:1

To find:

The velocity of sound in the mixture

Solution:

Let the volume of the oxygen be, x

The volume of hydrogen be, 4x

So, the total volume of the mixture, $V_m=5x$

Now, we can write mass of any object as, $m=\left(volume\right)density$

So, the total mass of the mixture will be,

$V_m\left({\rho }_m\right)=V_H{\rho }_H+V_o{\rho }_o$

$5x\left({\rho }_m\right)=4x\left({\rho }_H\right)+x\left(16\right)\left({\rho }_H\right)$

where,

${\rho }_o=\left(16\right)\left({\rho }_H\right)$

on solving we get,

${\rho }_m=4{\rho }_H$

Where,

$\left({\rho }_m\right)$is the density of mixture

${\rho }_H$ is the density of hydrogen

${\rho }_o$s the density of oxygen

Now, from the formula, the velocity of the sound in mixture can be written as

$v_{mix}=\sqrt{\frac{\gamma P}{{\rho }_m}}$ -------(i)

The velocity of sound in hydrogen which is v is written as,

$v=\sqrt{\frac{\gamma P}{{\rho }_H}}$ -------(ii)

Now dividing (i) by (ii), we get,

$\frac{v_{mix}}{v}=\frac{1}{2}$

$v_{mix}=\frac{v}{2}$

This implies that the velocity of the sound in the mixture is ½ times the velocity of sound in hydrogen.

So, the correct answer is option (C)