A sound wave having wavelength `lambda` forms stationary waves after reflection from a surface. The distance between two consecutive nodes is

Options

A. `lambda`
B. `lambda//2`
C. `lambda//4`
D. `lambda//8`

Answer

To solve the problem of finding the distance between two consecutive nodes in a stationary wave formed by a sound wave reflecting from a surface, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Stationary Waves**:
- A stationary wave is formed when two waves of the same frequency and amplitude travel in opposite directions and interfere with each other. In this case, one wave is traveling towards a rigid surface and reflects back.

2. **Identifying Nodes and Antinodes**:
- In a stationary wave, nodes are points where there is no displacement (the wave does not move), and antinodes are points where the displacement is maximum. The nodes occur at regular intervals along the wave.

3. **Wavelength Definition**:
- The wavelength (λ) is the distance between two consecutive points that are in phase (e.g., crest to crest or trough to trough).

4. **Relationship Between Wavelength and Nodes**:
- In a stationary wave, the distance between two consecutive nodes is half the wavelength. This is because a full wavelength consists of one complete cycle of the wave, which includes one node and one antinode.

5. **Calculating the Distance Between Nodes**:
- Since the distance between two consecutive nodes is half of the wavelength, we can express this mathematically as:
\[ \text{Distance between two nodes} = \frac{\lambda}{2} \]

6. **Conclusion**:
- Therefore, the distance between two consecutive nodes in the stationary wave formed by the reflection of the sound wave is \(\frac{\lambda}{2}\).

### Final Answer:
The distance between two consecutive nodes is \(\frac{\lambda}{2}\).