With the increase in humidity, the velocity of sound in air

Options

A. increases
B. decreases
C. first increases and then decreases
D. becomes infinite

Answer

To solve the question regarding the effect of humidity on the velocity of sound in air, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**: The velocity of sound in a medium is given by the formula:
\[ v = \sqrt{\frac{\gamma P}{\rho}} \]
where \( v \) is the velocity of sound, \( \gamma \) is the adiabatic index (which is constant for air), \( P \) is the pressure, and \( \rho \) is the density of the air.

2. **Effect of Humidity on Density**: When humidity increases, the amount of water vapor in the air increases. Since water vapor is less dense than the nitrogen and oxygen that make up the majority of dry air, the overall density of the air decreases as humidity increases.

3. **Analyzing the Formula**: From the formula for the velocity of sound, we see that the velocity is inversely proportional to the square root of the density:
\[ v \propto \frac{1}{\sqrt{\rho}} \]
This means that if the density \( \rho \) decreases, the velocity \( v \) must increase.

4. **Conclusion**: Since increasing humidity decreases the density of air, we conclude that the velocity of sound in air increases with an increase in humidity.

5. **Final Answer**: Therefore, the correct option is that the velocity of sound in air increases with the increase in humidity.