The velocity of sound in hydrogen is 1400ms−1. 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 Totalmass=2ρx3+16ρx3=18ρx3=6ρx) Density of the mixture =massvolume=16ρxx=6ρ Now vHvm=√ρmρ vH = velocity of sound in hydrogen = 1400ms−1 vm = velocity of sound in mixture =1400ms−1 ρm=6ρ ρH=ρ ∴1400vm=√6ρρ=2.45 vm=14002.45=571.4ms−1 Ans: 571.4ms−1