A tuning fork of frequency `256 H_(Z)` produces `4` beats per second with a wire of legth `25 cm` vibrating in its fundamental mode. The beat frequency decrease when the length is slightly shortened. What could be the minimum length by which the wire be shortened so that it produces no beats with the tuning fork?

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the relationship between frequency and length
The frequency \( f \) of a vibrating wire is inversely proportional to its length \( L \). This can be expressed as:
\[ f \propto \frac{1}{L} \]
This means that as the length of the wire decreases, the frequency increases.
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