The speed of sound in hydrogen at NTP is . Then the speed in a mixture of hydrogen and oxygen in the ratio of by volume will be:
Step 1: Given information
The speed of sound in hydrogen at NTP,
The ratio of hydrogen and oxygen by volume is .
Let,
V is the volume of oxygen.
4V is the volume of hydrogen.
d is the density of hydrogen.
D is the density of the mixture of gases.
The total volume of the mixture of hydrogen and oxygen will be:
and,
Density of oxygen
Step 2: To find
We have to find the speed of the mixture.
Step 3: Calculating the density of the mixture of gases
We know the formula,
Here,
m is the mass.
v is the velocity.
d is the density.
Now,
By substituting the given values, we get
Step 4: Calculation of the speed of the mixture
We know the speed of sound in the gas:
Because sound speed is inversely related to the square root of density, then
The ratio of the speed of mixture and hydrogen is:
By substituting the speed of sound in hydrogen in , we get
Therefore, option C is the correct choice.