Wave Mechanics Question 822

Question: If the density of oxygen is 16 times that of hydrogen, what will be the ratio of their corresponding velocities of sound waves

[KCET 1999]

Options:

A) 1 : 4

B) 4 : 1

C) 16 : 1

D) 1 : 16

Show Answer

Answer:

Correct Answer: A

Solution:

$ v=\sqrt{\frac{\gamma P}{\rho }}\Rightarrow \frac{{v _{O _{2}}}}{{v _{H _{2}}}}=\sqrt{\frac{{\rho _{H _{2}}}}{{\rho _{o _{2}}}}}=\sqrt{\frac{1}{16}}=\frac{1}{4} $