Velocity of sound in air
I. Increases with temperature
II. Decreases with temperature
III. Increase with pressure
IV. Is independent of pressure
V. 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 solve the question regarding the velocity of sound in air and its dependence on temperature and pressure, we will analyze each statement step by step.

### Step 1: Understanding the relationship between velocity of sound and temperature
The velocity of sound in a medium is affected by temperature. The formula for the velocity of sound (V) in an ideal gas can be expressed as:
\[ V = \sqrt{\frac{\gamma RT}{M}} \]
where:
- \( \gamma \) is the adiabatic index (ratio of specific heats),
- \( R \) is the universal gas constant,
- \( T \) is the absolute temperature,
- \( M \) is the molar mass of the gas.

From this formula, we can see that the velocity of sound (V) is directly proportional to the square root of the temperature (T). Therefore, as the temperature increases, the velocity of sound also increases.

**Conclusion for statement I:**
- **I. Increases with temperature**: This statement is **correct**.

### Step 2: Analyzing the opposite of the first statement
Since we established that the velocity of sound increases with temperature, the opposite statement must be false.

**Conclusion for statement II:**
- **II. Decreases with temperature**: This statement is **incorrect**.

### Step 3: Understanding the relationship between velocity of sound and pressure
Next, we need to analyze how pressure affects the velocity of sound. In the case of an ideal gas, the velocity of sound is independent of pressure. This is because while pressure can affect the density of the gas, it does not affect the speed of sound directly in an ideal gas scenario.

**Conclusion for statement III:**
- **III. Increase with pressure**: This statement is **incorrect**.

### Step 4: Confirming the independence of velocity of sound from pressure
Since the velocity of sound is independent of pressure in an ideal gas, we can conclude:

**Conclusion for statement IV:**
- **IV. Is independent of pressure**: This statement is **correct**.

### Step 5: Analyzing the independence from temperature
Lastly, we consider the statement regarding the independence of velocity of sound from temperature. Since we have already established that the velocity of sound does depend on temperature, this statement is false.

**Conclusion for statement V:**
- **V. Is independent of temperature**: This statement is **incorrect**.

### Final Conclusion
Based on the analysis:
- The correct statements are **I (Increases with temperature)** and **IV (Is independent of pressure)**.

Thus, the correct answer is:
**Only first and fourth are true.**