Question

the density of oxygen is 16 times the density of hydrogen. what is relation between the speed of sound the two gases in​

Answer 1

Answer:

The speed of sound in gas is inversely proportional to the square root of mass of gas. The atomic weight of oxygen is 16 and that of hydrogen is 1. Hence, the speed of sound in oxygen is less than in hydrogen (ratio of speed of sound in hydrogen to the oxygen is 4:1).

Answer 2

The speed of sound in sound in hydrogen is 4 times that of the speed of sound in oxygen.

Explanation:

It is given that, the density of oxygen is 16 times the density of hydrogen. We need to find the relation between the speed of sound in two gases. The speed of sound in terms of density is given by :

$v=\sqrt{\dfrac{B}{\rho}}$

$\rho_O=16\times \rho_H$

B is the bulk modulus

Let $\rho_O\ and\ \rho_H$ are the densities of oxygen and hydrogen/

For oxygen,

$v_O =\dfrac{B}{\sqrt{\rho_O} }$.........(1)

For hydrogen,

$v_H =\dfrac{B}{\sqrt{\rho_H} }$.......(2)

Dividing equation (1) and (2) as:

$\dfrac{v_O}{v_H}=\sqrt{\dfrac{\rho_H}{\rho_O}}\\\\\dfrac{v_O}{v_H}=\sqrt{\dfrac{\rho_H}{16\times \rho_H}}\\\\\dfrac{v_O}{v_H}=\sqrt{\dfrac{1}{16}}\\\\\dfrac{v_O}{v_H}=\dfrac{1}{4}\\\\v_H=4\times v_O$

So, the speed of sound in sound in hydrogen is 4 times that of the speed of sound in oxygen.

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