In a stationary wave along a string the strain is

Options

A. zero at the antinodes
B. maximum at the antinodes
C. zero at the nodes
D. maximum at the nodes

Answer

To solve the question regarding the strain in a stationary wave along a string, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Strain**:
Strain is defined as the change in length (elongation) of a material divided by its original length. Mathematically, it can be expressed as:
\[ \text{Strain} = \frac{\Delta L}{L_0} \]
where \(\Delta L\) is the change in length and \(L_0\) is the original length of the string.

2. **Visualize the Stationary Wave**:
A stationary wave is formed by the interference of two waves traveling in opposite directions. In a stationary wave, there are points called nodes (where there is no displacement) and antinodes (where the displacement is maximum).

3. **Identify the Points of Maximum and Minimum Displacement**:
- At the **nodes**, the displacement of the string is zero, meaning there is no elongation at these points.
- At the **antinodes**, the displacement is maximum, leading to maximum elongation.

4. **Determine the Strain at Nodes and Antinodes**:
- At the nodes, since there is no elongation (\(\Delta L = 0\)), the strain is also zero.
- At the antinodes, the elongation is maximum, which means the strain will be maximum at these points.

5. **Conclusion**:
Therefore, in a stationary wave along a string, the strain is maximum at the **antinodes**.

### Final Answer:
The strain in a stationary wave along a string is maximum at the antinodes.

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