Unlike a laboratory sonometer, a stringed instrument is seldom plucked in the middle. Supposing a sitar string is plucked at about `(1)/(4)th` of its length from the end. The most prominent harmonic would be

Options

A. Eighth
B. Fourth
C. Third
D. Second

Answer

To determine the most prominent harmonic when a sitar string is plucked at about \( \frac{1}{4} \)th of its length from the end, we can follow these steps:

### Step 1: Understand the setup
A sitar string is fixed at both ends, which means it can vibrate in certain modes or harmonics. When plucked, the string will form standing waves with nodes and antinodes.

### Step 2: Identify the point of plucking
Plucking the string at \( \frac{1}{4} \)th of its length from one end means that this point will be an antinode (the point of maximum displacement).

### Step 3: Determine the positions of nodes and antinodes
Since the string is fixed at both ends, the nodes will be at the ends (0 and L) and at the midpoint (L/2). Given that we have an antinode at \( \frac{1}{4}L \), we can visualize the standing wave pattern:
- Antinode at \( \frac{1}{4}L \)
- Node at \( \frac{1}{2}L \)
- Antinode at \( \frac{3}{4}L \)
- Node at L

### Step 4: Count the number of loops
In this configuration, we can see that there are two antinodes and three nodes:
- The first antinode is at \( \frac{1}{4}L \)
- The second antinode is at \( \frac{3}{4}L \)

This configuration corresponds to the second harmonic, which has one complete loop (or segment) between the two nodes.

### Step 5: Conclusion
Thus, the most prominent harmonic when the sitar string is plucked at \( \frac{1}{4} \)th of its length from the end is the **second harmonic**.

### Final Answer
The most prominent harmonic would be the **second harmonic**.

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