Question

Under the same conditions of pressure and temperature, the velocity of sound in oxygen and hydrogen gases are $v_o$ and $v_H$ , then

• A. $v_H=v_o$
  
• B. $v_H=4v_o$
  
• C. $v_o=4V_H$
  
• D. $v_H=16v_o$
  

Answer 1

The correct option is B $v_H=4v_o$

Velocity of sound in gas $v=\sqrt{\frac{\gamma RT}{M}}$

$⟹$ $v\propto \sqrt{\frac{1}{M}}$

where $M$ is the molar mass of the gas.

Thus we get $\frac{v_H}{v_o}=\sqrt{\frac{M_o}{M_H}}$

Or $\frac{v_H}{v_o}=\sqrt{\frac{32}{2}}=4$

$⟹v_H=4v_o$