Velocity of sound in air
(I) increases with temperature
(II) decreases with temperature
(III) increase with pressure
(IV) is independent of pressure
(V) decreases with pressure
(VI) is independent of temperature Choose the correct answer

Options

A. only I and II are true
B. only I and III are true
C. only II and III are true
D. only I and IV are true

Answer

To determine the correct statements regarding the velocity of sound in air, we need to analyze each statement based on the principles of physics.

### Step-by-Step Solution:

1. **Understanding the Relationship**: The velocity of sound in a medium can be expressed using the formula:
\[ v = \sqrt{\frac{\gamma RT}{M}} \]
where \( v \) is the velocity of sound, \( \gamma \) is the adiabatic index, \( R \) is the universal gas constant, \( T \) is the absolute temperature, and \( M \) is the molar mass of the gas.

2. **Analyzing Statement (I)**:
- **Statement**: "Velocity of sound in air increases with temperature."
- **Analysis**: Since the formula shows that \( v \) is proportional to the square root of temperature \( T \), as temperature increases, the velocity of sound also increases.
- **Conclusion**: This statement is **true**.

3. **Analyzing Statement (II)**:
- **Statement**: "Velocity of sound in air decreases with temperature."
- **Analysis**: This contradicts our conclusion from Statement (I). As temperature increases, the velocity does not decrease.
- **Conclusion**: This statement is **false**.

4. **Analyzing Statement (III)**:
- **Statement**: "Velocity of sound in air increases with pressure."
- **Analysis**: The formula indicates that the velocity of sound is independent of pressure for an ideal gas at constant temperature. Therefore, changing pressure does not affect the velocity.
- **Conclusion**: This statement is **false**.

5. **Analyzing Statement (IV)**:
- **Statement**: "Velocity of sound in air is independent of pressure."
- **Analysis**: As established, the velocity of sound does not depend on pressure in an ideal gas scenario.
- **Conclusion**: This statement is **true**.

6. **Analyzing Statement (V)**:
- **Statement**: "Velocity of sound in air decreases with pressure."
- **Analysis**: This is also false since the velocity does not change with pressure.
- **Conclusion**: This statement is **false**.

7. **Analyzing Statement (VI)**:
- **Statement**: "Velocity of sound in air is independent of temperature."
- **Analysis**: This contradicts our analysis of Statement (I) where we found that velocity increases with temperature.
- **Conclusion**: This statement is **false**.

### Final Conclusion:
From the analysis, the true statements are:
- Statement (I): True
- Statement (IV): True

Thus, the correct answer is that only statements (I) and (IV) are true.

### Correct Answer:
**Option 4**: Only statements 1 and 4 are true.