To solve the question regarding the independence of the velocity of sound in air from various factors, we can analyze the relationships involved step by step.
### Step-by-Step Solution:
1. **Understanding the Formula for Velocity of Sound**:
The velocity of sound in air can be expressed using the formula:
\[
v = \sqrt{\frac{\gamma P}{\rho}}
\]
where:
- \( v \) is the velocity of sound,
- \( \gamma \) is the ratio of specific heats (\( \frac{C_p}{C_v} \)),
- \( P \) is the pressure,
- \( \rho \) is the density of air.
2. **Analyzing the Effect of Temperature**:
The velocity of sound is influenced by temperature. The relationship can be expressed as:
\[
v = \sqrt{\frac{\gamma R T}{M}}
\]
where \( R \) is the gas constant, \( T \) is the absolute temperature, and \( M \) is the molecular weight. Since \( T \) changes with temperature, the velocity of sound is dependent on temperature.
3. **Analyzing the Effect of Pressure and Density**:
According to the ideal gas law:
\[
PV = nRT
\]
If we increase the pressure \( P \) while keeping the temperature constant, the volume \( V \) decreases, which increases the density \( \rho \). Thus, as pressure increases, density also increases, keeping the ratio \( \frac{P}{\rho} \) constant. Therefore, the velocity of sound remains independent of changes in pressure and density.
4. **Analyzing the Effect of Humidity**:
Humidity introduces water vapor into the air, which has a lower molecular weight than the gases it replaces (like oxygen or nitrogen). When water vapor replaces these heavier gases, the average molecular weight of the air decreases, leading to an increase in the velocity of sound. Thus, the velocity of sound is not independent of humidity.
5. **Conclusion**:
From the analysis, we conclude that the velocity of sound in air is independent of changes in pressure and density, but it is dependent on temperature and humidity.
### Final Answer:
The velocity of sound in air is independent of changes in **pressure and density**.
