A stone is hung from a sonometer wire. If the stone is immersed in water the fundamental frequency

Options

A. increases
B. decreases
C. remains same
D. becomes erratic

Answer

To solve the problem regarding the fundamental frequency of a sonometer wire when a stone is immersed in water, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Fundamental Frequency Formula**:
The fundamental frequency (f) of a vibrating string or wire is given by the formula:
\[ f = \frac{1}{2L} \sqrt{\frac{T}{m}} \]
where:
- \( L \) = length of the wire
- \( T \) = tension in the wire
- \( m \) = mass per unit length of the wire

2. **Identify the Forces Acting on the Stone**:
When the stone is hung from the sonometer wire, two forces act on it:
- The downward gravitational force (weight) \( mg \)
- The upward buoyant force \( F_b \) when the stone is immersed in water

3. **Determine the Effect of Buoyant Force**:
When the stone is immersed in water, the buoyant force reduces the effective weight of the stone. The new effective tension \( T' \) in the wire can be expressed as:
\[ T' = mg - F_b \]
where \( F_b \) is the buoyant force acting on the stone.

4. **Analyze the Change in Tension**:
Since the buoyant force acts upward, it reduces the tension in the wire. Therefore, the new tension \( T' \) will be less than the original tension \( T \):
\[ T' < T \]

5. **Impact on Fundamental Frequency**:
Since the fundamental frequency is directly proportional to the square root of the tension, a decrease in tension leads to a decrease in the fundamental frequency:
\[ f' = \frac{1}{2L} \sqrt{\frac{T'}{m}} < \frac{1}{2L} \sqrt{\frac{T}{m}} = f \]
Thus, the fundamental frequency decreases when the stone is immersed in water.

6. **Conclusion**:
The correct answer is that the fundamental frequency decreases when the stone is immersed in water.

### Final Answer:
The fundamental frequency decreases when the stone is immersed in water.