Question

The speed of sound in Hydrogen at NTP, is 1270 m/s. Then the speed in a mixture of Hydrogen and Oxygen in the ratio 4:1 by volume, (in m/s) will be

Answer 1

Let the volume of oxygen be V 
then the volume of Hydrogen be 4V 
so, total volume of mixture of Hydrogen and oxygen = 4V + V = 5V 

now, mass of mixture = mass of Hydrogen + mass of oxygen 

volume of mixture × density of mixture = volume of Hydrogen × density of Hydrogen + volume of oxygen × density of oxygen 

5V × D = 4V × d + V × 16d [ actually, density is directly proportional to molar mass of element , so, density of Hydrogen = 16 × density of oxygen ] 
Where D is density of mixture , d is the density of Hydrogen.
so, D = 4d 
means , density of mixture is 4 times of density of Hydrogen .

now, speed of sound in the mixture, 
$\bold{V_{mix} = \sqrt \frac{\gamma P}{D}}$

γ is same for mixture because both the gas in the mixture { Hydrogen and oxygen } are diamagnetic . 
so, speed of sound in the Hydrogen ,
$\bold{V_{H_2}= \sqrt\frac{\gamma P}{d}}$


$now, \bold{\frac{V_{mix}}{V_{H_2}}=\sqrt{\frac{d}{D}}}$

now, you should use D = 4d , 
$then, \bold{V_{mix}=\frac{V_{H_2}}{2}}$

$\bold{ V_{mix}=\frac{1270}{2}=635m/s}$