Physics - Sound Wave Question with Solution | TestHub

The speed of sound in a gas is given by $v=\sqrt{\frac{\gamma RT}{M}}$, where $M$ is the molar mass of the gas.

Dry air consists mainly of nitrogen ($N_2$, molar mass $28$ g/mol) and oxygen ($O_2$, molar mass $32$ g/mol), giving an average molar mass of approximately $28.97$ g/mol.

Water vapor ($H_{2}O$) has a molar mass of $18$ g/mol. When humidity increases, water vapor displaces heavier nitrogen and oxygen molecules, which decreases the average molar mass $M$ of the air.

Since the speed of sound is inversely proportional to the square root of the molar mass ($v\propto \frac{1}{\sqrt{M}}$), a decrease in molar mass leads to an increase in the speed of sound.

Thus, when humidity increases, the speed of sound waves is more.

Answer: Speed of sound waves is more.