A second harmonic has to be generated in a string of length l stretched between two rigid supports. The point where the string has to be plucked and touched are

Options

A. Plucked at `l//4` and touch at `l//2`
B. Plucked at `l//4` and touch at `3l//4`
C. Plucked at `l//2` and touched at `l//4`
D. Plucked at `l//2` and touched at `3l//4`

Explanation

To solve the problem of generating a second harmonic in a string of length \( L \) stretched between two rigid supports, we need to understand the characteristics of harmonics in a vibrating string.

### Step-by-Step Solution:

1. **Understanding the Second Harmonic**:
- The second harmonic of a string corresponds to the formation of two loops (or segments) between the fixed ends. This means that there will be one node at each end and one node in the middle, with two antinodes.

2. **Identifying Nodes and Antinodes**:
- In the second harmonic, the nodes are located at the ends of the string and at the midpoint. The antinodes are located at \( \frac{L}{4} \) and \( \frac{3L}{4} \) along the length of the string.

3. **Determining the Plucking Point**:
- To generate the second harmonic, the string must be plucked at a point where it can vibrate in the desired mode. For the second harmonic, the string should be plucked at \( \frac{L}{4} \) from one end. This is where the first antinode is located.

4. **Determining the Touching Point**:
- The string must be touched (or damped) at the midpoint to create the necessary nodes. This means that the string should be touched at \( \frac{L}{2} \).

5. **Final Answer**:
- Therefore, to generate the second harmonic in a string of length \( L \) stretched between two rigid supports, the string should be plucked at \( \frac{L}{4} \) and touched at \( \frac{L}{2} \).

### Summary:
- Plucking Point: \( \frac{L}{4} \)
- Touching Point: \( \frac{L}{2} \)