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

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 (A)  √8  (B)  √2/17  (C)  √1/8  (D)  √32/17

Tardigrade Admin · Accepted Answer

Let one mole of each gas has same volume as

V

.
When they are mixed, then density of mixture is

ρ_{mixture} = \frac{mass of O _{2} + mass of H _{2}}{volume of O _{2} + volume of H _{2}}

= \frac{32 + 2}{V + V} = \frac{34}{2 V} = \frac{17}{V}

Also,

ρ_{H_{2}} = \frac{2}{V}

Now, velocity

v = (\frac{γ P}{ρ})^{1/2}

or

v \propto \frac{1}{ρ}

\frac{v _{mixture}}{v _{H_{2}}} = (\frac{ρ _{H_{2}}}{ρ _{mixture}})

= (\frac{2/ V}{17/ V}) = (\frac{2}{17})

Q. 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

$8$

$2/17$

$1/8$

$32/17$

Q. 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

8​

2/17​

1/8​

32/17​

Q. 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

$8$

$2/17$

$1/8$

$32/17$