Which of the following statements is not true about a sound wave ?

Options

A. Sound travels faster in steel than in air.
B. Sound is a longitudinal wave.
C. The speed of sound in gas is not affected by a change in pressure of the gas.
D. The speed of sound in a gas decreases with increase in the temperature of the gas.

Explanation

To determine which statement is not true about sound waves, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement Analysis**: The first statement is: "Sound travels faster in steel than in air."
- **Explanation**: Sound travels fastest in solids, followed by liquids, and slowest in gases. Since steel is a solid and air is a gas, this statement is true.

2. **Statement Analysis**: The second statement is: "Sound is a longitudinal wave."
- **Explanation**: Sound waves are indeed longitudinal waves, meaning the vibrations of the particles in the medium are parallel to the direction of the wave's propagation. This statement is also true.

3. **Statement Analysis**: The third statement is: "The speed of sound in gas is not affected by the change in pressure."
- **Explanation**: The speed of sound in a gas can be expressed as \( v = \sqrt{\frac{\gamma P}{\rho}} \). However, when pressure increases in a gas, density also increases, keeping the ratio \( \frac{P}{\rho} \) constant at a constant temperature. Therefore, this statement is true.

4. **Statement Analysis**: The fourth statement is: "The speed of sound decreases with an increase in temperature."
- **Explanation**: The speed of sound in a gas is given by the formula \( v = \sqrt{\frac{\gamma RT}{M}} \), where \( T \) is the temperature. As temperature increases, the speed of sound also increases. Therefore, this statement is false.

### Conclusion:
The statement that is not true about sound waves is: **"The speed of sound decreases with an increase in temperature."**

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