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Question

Speed of sound in air is 332 m/s at NTP. What will be the speed of sound in hydrogen at NTP if the density of hydrogen at NTP is (1/16) that of air?

A
664 m/s
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B
1328 m/s
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C
1155 m/s
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D
166 m/s
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Solution

The correct option is B 1328 m/s
The velocity of sound in a medium is given by
v=γPρ
Velocity of sound in air is
vair=γairPairρair ...(i)
Velocity of sound in hydrogen is
vH=γHPHρH ...(ii)

From equation (i) and (ii)
vHvair=PHρH×ρairPair=ρairρH
(as Pair=PH)
(Here, γair=γH as hydrogen is a diatomic gas and air is mainly a mixture of diatomic gases.)
vH=vair×ρairρH=332×161=1328 m/s

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