The velocity of sound in gas is independent of

Options

A. pressure
B. temperature
C. density
D. humidity

Explanation

To determine what the velocity of sound in a gas is independent of, we can analyze the factors that influence it. The velocity of sound in a gas can be expressed using the formula:

\[ v = \sqrt{\frac{\gamma P}{\rho}} \]

Where:
- \( v \) is the velocity of sound,
- \( \gamma \) is the adiabatic index (ratio of specific heats),
- \( P \) is the pressure of the gas,
- \( \rho \) is the density of the gas.

### Step-by-Step Solution:

1. **Identify the Variables**: The formula shows that the velocity of sound depends on pressure (\( P \)), density (\( \rho \)), and the adiabatic index (\( \gamma \)).

2. **Analyze the Effect of Pressure**:
- If we increase the pressure of the gas, the density also changes. According to the ideal gas law (\( PV = nRT \)), if pressure increases while the temperature remains constant, the density will also increase. Thus, the ratio \( \frac{P}{\rho} \) remains constant. Therefore, the velocity of sound does not change with pressure.

3. **Analyze the Effect of Density**:
- The velocity of sound is directly influenced by density. If the density of the gas changes (for example, by changing the medium or increasing humidity), the velocity of sound will change accordingly.

4. **Analyze the Effect of Temperature**:
- The velocity of sound is also dependent on temperature. As temperature increases, the kinetic energy of the gas molecules increases, leading to an increase in the velocity of sound. This can be seen from the rearranged formula \( v = \sqrt{\frac{\gamma RT}{M}} \), which shows that velocity is proportional to the square root of temperature.

5. **Conclusion**:
- From the analysis, we can conclude that the velocity of sound in a gas is independent of pressure. It is dependent on density and temperature.

### Final Answer:
The velocity of sound in a gas is independent of **pressure**.