Phase difference between a particle at a compre-ssion and a particle at the next rarefaction is

Options

A. Zero
B. `pi//2`
C. `pi`
D. `pi//4`

Explanation

To solve the problem of finding the phase difference between a particle at compression and a particle at the next rarefaction, we can follow these steps:

### Step 1: Understand the Concepts of Compression and Rarefaction
- **Compression** is a region in a sound wave where particles are close together, resulting in higher pressure.
- **Rarefaction** is a region where particles are spread apart, resulting in lower pressure.

### Step 2: Visualize the Wave
- A sound wave can be represented as a sinusoidal wave. In this wave, the peaks represent compressions, and the troughs represent rarefactions.

### Step 3: Identify the Positions
- In a sinusoidal wave, the displacement of particles oscillates between positive and negative values.
- A compression occurs at the peak (maximum positive displacement), while the next rarefaction occurs at the trough (maximum negative displacement).

### Step 4: Determine the Phase Difference
- The phase of a wave can be described in terms of radians. A complete cycle of a wave corresponds to \(2\pi\) radians.
- The distance from a compression (peak) to the next rarefaction (trough) is half of a complete cycle. Therefore, the phase difference between a compression and the next rarefaction is:
\[ \text{Phase Difference} = \pi \text{ radians} \]

### Conclusion
- The phase difference between a particle at compression and a particle at the next rarefaction is \( \pi \) radians.