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A sample of oxygen at NTP has volume V and a sample of hydrogen at NTP has the volume 4V Both the gases are mixed. If the speed of sound in hydrogen at NTP is 1270 m/s, that in mixture is

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317 m / s

635 m/s

830 m/s

950 m/s

answer is B.

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Detailed Solution

$ρ_{mix} = \frac{m_{1} + m_{2}}{v_{1} + v_{2}}$

$ρ_{mix} = \frac{ρ_{H} V_{H} + ρ_{0} V_{0}}{V + 4 V} = \frac{ρ_{H} 4 V + 16 ρ_{H} V}{5 V}$

$ρ_{mix} = \frac{20 ρ_{H} V}{5 V} = 4 ρ_{H}$

$V \propto \sqrt{\frac{1}{ρ}} \Rightarrow \frac{V_{mix}}{V_{H}} = \sqrt{\frac{ρ_{H}}{4 ρ_{H}}}$

$V_{mix} = \frac{1270}{2} = 635 m / s$

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