First slide

Travelling wave

Question

Oxygen is 16 times heavier than hydrogen. Equal volumes of hydrogen and oxygen are mixed. The ratio of speed of sound in the mixture to that in hydrogen is

Easy

A

$\sqrt{\frac{1}{8}}$
B

$\sqrt{\frac{32}{17}}$
C

$\sqrt{8}$
D

$\sqrt{\frac{2}{17}}$

Solution

Density of mixture $= ρ_{mix} = \frac{V_{O_{2}} ρ_{O_{2}} + V_{H_{2}} ρ_{H_{2}}}{V_{O_{2}} + V_{H_{2}}}$
$= \frac{V (ρ_{O_{2}} + ρ_{H_{2}})}{2 V} = \frac{ρ_{O_{2}} + ρ_{H_{2}}}{2} (since V_{O_{2}} = V_{H_{2}} = V)$
$= \frac{ρ_{H_{2}} + 16 ρ_{H_{2}}}{2} = 8 .5 ρ_{H_{2}} \Rightarrow v \propto \frac{1}{\sqrt{ρ}}$
$\Rightarrow \frac{V_{mix}}{V_{H_{2}}} = \sqrt{\frac{ρ_{H_{2}}}{ρ_{mix}}} = \sqrt{\frac{ρ_{H_{2}}}{8 .5 ρ_{H_{2}}}} \approx \sqrt{\frac{1}{8}}$

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