The linear distance between a consecutive compression and a rarefaction in longitudinal wave is :

Options

A. `lambda`
B. `(lambda)/(2)`
C. `(lambda)/(4)`
D. `(3lambda)/(4)`

Explanation

To solve the problem, we need to understand the concept of longitudinal waves and how they are characterized by compressions and rarefactions.

### Step-by-Step Solution:

1. **Understand Longitudinal Waves**: In a longitudinal wave, particles of the medium move parallel to the direction of the wave. This results in areas of compression (where particles are close together) and rarefaction (where particles are spread apart).

2. **Identify Wavelength**: The wavelength (λ) of a longitudinal wave is defined as the distance between two successive compressions or two successive rarefactions.

3. **Determine Distance Between Compression and Rarefaction**: The distance between a compression and the nearest rarefaction is half of the wavelength. This is because one full wavelength consists of one compression followed by one rarefaction, and then another compression.

4. **Calculate the Distance**: Therefore, the linear distance between a consecutive compression and a rarefaction is given by:
\[ \text{Distance} = \frac{\lambda}{2} \]

5. **Conclusion**: The answer to the question is that the linear distance between a consecutive compression and a rarefaction in a longitudinal wave is \(\frac{\lambda}{2}\).

### Final Answer:
The linear distance between a consecutive compression and a rarefaction in a longitudinal wave is \(\frac{\lambda}{2}\).