During propagation of longitudinal wave, if at any time, there is compression at a point, after how much time there will be rarefaction?

Options

A. T
B. `T/3`
C. `T/4`
D. `T/2`

Explanation

To solve the question, "During the propagation of a longitudinal wave, if at any time there is compression at a point, after how much time will there be rarefaction?", we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Wave Motion**:
- In a longitudinal wave, particles of the medium oscillate back and forth in the direction of the wave propagation. This creates regions of compression (where particles are close together) and rarefaction (where particles are spread apart).

2. **Identify the Cycle of the Wave**:
- A complete cycle of a longitudinal wave consists of one compression followed by one rarefaction and then back to another compression.

3. **Define the Time Period (T)**:
- The time it takes for one complete cycle of the wave is called the time period (T).

4. **Determine the Time from Compression to Rarefaction**:
- From the point of maximum compression to the point of maximum rarefaction is half of the time period (T/2).
- However, since we are interested in the time taken to go from compression to the next rarefaction, we can break it down further.

5. **Break Down the Time Period**:
- The time taken to go from compression to the next rarefaction can be divided into two parts:
- From compression to the midpoint (which is a quarter of the time period, T/4).
- From the midpoint to rarefaction (which is another quarter of the time period, T/4).

6. **Calculate Total Time**:
- Therefore, the total time taken from compression to rarefaction is:
\[ T/4 + T/4 = T/2 \]

7. **Conclusion**:
- Thus, if there is compression at a point, after a time of \( T/2 \), there will be rarefaction at that point.

### Final Answer:
The time after which there will be rarefaction following compression is \( T/2 \).

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