Velocity of sound in air
(i) increases with temperature
(ii) decreases with temperature
(iii) increases with pressure
(iv) is independent of pressure

Options

A. (i) and (ii)
B. (i) and (iii)
C. (ii) and (iii)
D. (i) and (iv)

Answer

To determine how the velocity of sound in air is affected by temperature and pressure, we can analyze the relationship using the formula for the speed of sound in an ideal gas.

### Step-by-Step Solution:

1. **Understanding the Formula**:
The speed of sound (V) in an ideal gas can be expressed as:
\[ V = \sqrt{\frac{\gamma P}{\rho}} \]
where \( \gamma \) is the adiabatic index (ratio of specific heats), \( P \) is the pressure, and \( \rho \) is the density of the gas.

2. **Effect of Temperature on Density**:
The density (\( \rho \)) of air decreases with an increase in temperature. According to the ideal gas law:
\[ PV = nRT \]
As temperature (T) increases, for a constant pressure, the density (\( \rho \)) decreases.

3. **Velocity and Temperature**:
As the temperature increases, the decrease in density (\( \rho \)) leads to an increase in the speed of sound (V). Therefore, we can conclude that:
\[ V \text{ increases with temperature.} \]

4. **Effect of Pressure**:
When considering the effect of pressure on the speed of sound, if we keep the temperature constant, we can see that:
\[ V = \sqrt{\frac{\gamma P}{\rho}} \]
If pressure increases while temperature remains constant, the density also increases (since \( P \) and \( T \) are directly related). However, the increase in pressure does not significantly affect the speed of sound because the density increases proportionately.

5. **Conclusion on Pressure**:
Therefore, the speed of sound is independent of pressure when temperature is constant. Thus, we can conclude:
\[ V \text{ is independent of pressure.} \]

### Final Answers:
- (i) Increases with temperature: **True**
- (ii) Decreases with temperature: **False**
- (iii) Increases with pressure: **False**
- (iv) Is independent of pressure: **True**