(A): According to Laplace the propagation of sound in air is an adiabatic process.
(B): Pressure has no effect on velocity of sound in a gas as long as temperature remains constant.
(C): The velocity of sound in air changes by 0.61 m/s when temperature changes by `1^(@)C`

Options

A. All are true
B. A,B are only true
C. B are true
D. A,C are only true

Answer

To solve the question, we need to evaluate the three statements regarding the propagation of sound in air. Let's analyze each statement step by step.

### Statement A:
**According to Laplace, the propagation of sound in air is an adiabatic process.**

1. **Understanding Adiabatic Process**: An adiabatic process is one in which no heat is exchanged with the surroundings. In the context of sound propagation, this means that the temperature of the medium changes during the compression and rarefaction of sound waves.

2. **Laplace's Assumption**: Laplace proposed that sound waves in air propagate as an adiabatic process, where the temperature increases during compression and decreases during rarefaction, but the total heat remains constant.

3. **Conclusion**: This statement is **true** because Laplace's theory correctly describes sound propagation as an adiabatic process.

### Statement B:
**Pressure has no effect on the velocity of sound in a gas as long as temperature remains constant.**

1. **Velocity of Sound Formula**: The velocity of sound \( v \) in a gas is given by the formula:
\[ v = \sqrt{\frac{\gamma P}{\rho}} \]
where \( \gamma \) is the ratio of specific heats, \( P \) is the pressure, and \( \rho \) is the density of the gas.

2. **Ideal Gas Law**: According to the ideal gas law \( PV = nRT \), we can express density \( \rho \) as \( \rho = \frac{m}{V} \), which implies that pressure and density are related.

3. **Effect of Pressure**: If temperature is constant, any increase in pressure will increase density proportionally, thus maintaining the ratio \( \frac{P}{\rho} \) constant. Therefore, pressure does not affect the velocity of sound in an isothermal process.

4. **Conclusion**: This statement is **true** because, under constant temperature, pressure does not affect the velocity of sound.

### Statement C:
**The velocity of sound in air changes by 0.61 m/s when temperature changes by 1°C.**

1. **Temperature and Velocity Relationship**: The velocity of sound is directly proportional to the square root of the absolute temperature (in Kelvin):
\[ v \propto \sqrt{T} \]

2. **Standard Values**: At 0°C (273 K), the velocity of sound is approximately 330 m/s.

3. **Calculating Change**: If the temperature increases by 1°C (from 273 K to 274 K):
\[ v_{new} = v_{old} \times \sqrt{\frac{T_{new}}{T_{old}}} = 330 \times \sqrt{\frac{274}{273}} \]

4. **Calculating the Result**: After performing the calculation:
\[ v_{new} \approx 330.61 \, \text{m/s} \]
The change in velocity is:
\[ \Delta v = v_{new} - v_{old} = 330.61 - 330 = 0.61 \, \text{m/s} \]

5. **Conclusion**: This statement is **true** as the velocity of sound indeed changes by 0.61 m/s for a temperature change of 1°C.

### Final Conclusion:
All three statements (A, B, and C) are **true**.

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