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 ______.

Options

• `sqrt(1/8)`

• `sqrt(32/77)`

• `sqrt8`

• `sqrt(2/17)`

Answer 1

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 `underlinebb(sqrt(2/17))`.

Explanation:

Let V₂ = Speed of sound in the mixture of oxygen and hydrogen,

V₁ = Speed of sound in hydrogen,

ρ_H = Density of hydrogen atom,

ρ_M = Density of mixture,

v = Volume of gases, and Mass of the hydrogen atom (M_H) = 2 amu

The ratio of speeds between the mixture and hydrogen can be written as

⇒ `"V"_2/"V"_1=sqrt((rho"H")/(rho"M"))`

The density of hydrogen ρ_H 

⇒ ρ_H = `"M"_"H"/"v"=2/"v"`

The density of the mixture is given by

⇒ ρ_M = `"M"_"m"/"v"=(16+1)/"v"=17/"v"`

Substituting the values of ρ_M, ρ_H in equation 1

⇒  `"V"_2/"V"_1=sqrt(2/17)`