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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
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B
2v
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C
v/2
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D
v/4
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Solution

The correct option is B 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, Vm=5x

Now, we can write mass of any object as, m=(volume)density
So, the total mass of the mixture will be,

Vm(ρm)=VHρH+Voρo
5x(ρm)=4x(ρH)+x(16)(ρH)

where,
ρo=(16)(ρH)

on solving we get,
ρm=4ρH

Where,
(ρm)is the density of mixture
ρH is the density of hydrogen
ρos the density of oxygen

Now, from the formula, the velocity of the sound in mixture can be written as
vmix=γPρm -------(i)

The velocity of sound in hydrogen which is v is written as,
v=γPρH -------(ii)
Now dividing (i) by (ii), we get,

vmixv=12

vmix=v2

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)






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