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Question
Hydrogen gas is filled in two identical bottles, A and B, at the same temperature. The mass of hydrogen in the two bottles is 12 gm and 48 gm respectively. In which bottle will sound travel faster? How many times be as fast as the other?
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Solution
Mass of hydrogen in bottle A = w1 = 12gm
Mass of hydrogen in bottle B = w2 = 48gm
∴ Density ∝ mass
`"P"_1/"P"_2="w"_1/"w"_2` and for velocity `"v" ∝ 1/sqrt(ρ)∝1/sqrt"w"`
∴ `"v"_1/"v"_2 = sqrt("P"_2/"P"_1) = sqrt("w"_2/"w"_1)= sqrt((48)/(12)) = sqrt(4/1) = 2/1`
Hence, Sound will travel faster in bottle A and the speed will be twice as that of bottle B.
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