A student plotted the following four graphs representing the variation of velocity of sound in a gas with the pressure P. Which one is correct?

Options

A.
B.
C.
D.

Explanation

To determine the correct graph representing the variation of the velocity of sound in a gas with pressure, we need to analyze the relationship between these two variables based on the principles of physics.

### Step-by-Step Solution:

1. **Understanding the Variables**:
- The velocity of sound in a gas is influenced by various factors, primarily temperature. The formula for the velocity of sound \( v \) in a gas is given by:
\[ v = \sqrt{\frac{\gamma \cdot R \cdot T}{M}} \]
where \( \gamma \) 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. **Identifying the Effect of Pressure**:
- When considering the effect of pressure on the velocity of sound, it is important to note that if the temperature is held constant, the pressure does not directly affect the velocity of sound. This is because, at constant temperature, the density of the gas changes with pressure, but the effect on the speed of sound is negligible.

3. **Analyzing the Graphs**:
- The question provides four graphs that depict the relationship between the velocity of sound and pressure. We need to identify which graph shows that the velocity remains constant regardless of changes in pressure.

4. **Selecting the Correct Graph**:
- The correct graph should show a horizontal line, indicating that the velocity of sound does not change with pressure when the temperature is constant. This corresponds to the idea that pressure is independent of the velocity of sound under these conditions.

5. **Conclusion**:
- Based on the analysis, the correct graph is the one that shows a constant velocity of sound regardless of changes in pressure. This is represented by option 4, which indicates that the velocity of sound remains uniform as pressure varies.

### Final Answer:
- The correct graph representing the variation of velocity of sound in a gas with pressure is **Option 4**.