A sonometer wire of certain length is stretched under a tension of 5 kgf and vibrates in unison with a tuning fork of unknown frequency. When the tension is changed to 4 kgf, it produces 5 beats per second with the tuning fork. Determine the frequency of tuning fork.

Explanation

To determine the frequency of the tuning fork using the information provided, we can follow these steps:

### Step 1: Understand the relationship between tension and frequency
The frequency of a vibrating string (or sonometer wire) is given by the formula:
\[ f = \frac{1}{2L} \sqrt{\frac{T}{M}} \]
where:
- \( f \) = frequency of the wire
- \( L \) = length of the wire (constant)
...