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Question

The velocity of sound in hydrogen is 1400 ms1. What will be the velocity of sound in a mixture of gases having two parts by volume of hydrogen and one part by volume of oxygen. Maintaing the same pressure?

A
371.4 m/s
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B
471.4 m/s
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C
571.4 m/s
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D
671.4 m/s
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Solution

The correct option is C 571.4 m/s
Let ρH be the density of hydrogen and ρ the density of oxygen. Then ρ=16ρH.
Let x be the volume of the mixture
Volume of hydrogen in the mixture =2x3
Volume oxygen in the mixture =x3
Mass of hydrogen in the mixture =(2x3)ρ
Mass of oxygen in the mixture =(2x3)ρ0=(x3)16ρ
Total mass=2 ρx3+16 ρx3=18ρx3=6ρx)
Density of the mixture =massvolume=16ρxx=6ρ
Now vHvm=ρmρ
vH = velocity of sound in hydrogen = 1400ms1
vm = velocity of sound in mixture =1400 ms1
ρm=6ρ
ρH=ρ
1400vm=6ρρ=2.45
vm=14002.45=571.4 ms1
Ans: 571.4 ms1

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