A wire is in uniform with a tuning fork when stretched by a weight of density `9000 kg//m^(3)` in a sonometer experiment . When the weight is immersed in water , the same wire produces ` 5 beats//s` with the same fork. Find the frequency of the fork.

Explanation

To solve the problem, we need to analyze the situation step by step, focusing on the relationship between tension, frequency, and the effects of buoyancy when the weight is immersed in water.

### Step-by-Step Solution:

1. **Understanding the Initial Setup**:
- The wire is initially under tension \( T = mg \) where \( m \) is the mass of the weight and \( g \) is the acceleration due to gravity.
- The frequency of the wire when the weight is hanging in air is given by \( f \).

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