Question

the ratio of the velocity of sound in hydrogen to the velocity of sou d in oxygen​

Answer 1

velocity of sound in hydrogen is 1270:/

and velocity of sound in oxygen is 326m /s

therefore the ratio will be 1270/326

I.e 635:163

Answer 2

Velocity of sound in a gas of molecular mass M is given by,

$\sf{\longrightarrow v=\sqrt{\dfrac{\gamma RT}{M}}}$

where $\gamma$ is adiabatic constant or heat capacity ratio, R is universal gas constant and T is temperature.

At constant temperature and same adiabatic constant (about compound containing same no. of atoms),

$\sf{\longrightarrow v\propto\dfrac{1}{\sqrt M}}$

R is also a constant.

Therefore,

$\sf{\longrightarrow\dfrac{v_1}{v_2}=\sqrt{\dfrac{M_2}{M_1}}}$

According to the question,

• molecular mass of Hydrogen, $\sf{M_1=2\ g\ mol^{-1}.}$

• molecular mass of Oxygen, $\sf{M_2=32\ g\ mol^{-1}.}$

Therefore, ratio of velocities of sound in each will be,

$\sf{\longrightarrow\dfrac{v_1}{v_2}=\sqrt{\dfrac{32}{2}}}$

$\sf{\longrightarrow\underline{\underline{\dfrac{v_1}{v_2}=4}}}$