When 0.98m long metallic wire is stressed, an extension of 0.02 m is produced. An organ pipe 0.5 m long and open at both ends, when sounded with this stressed metallic wire, produces 8 beats in its fundamental mode. By decreasing the stress in the wire, the number of beats are found to decrease. Find the young's modulus of wire. The density of metallic wire is `10^(4)kg//m^(3)` and sound velocity in the air is 292 m/s.

Explanation

To find the Young's modulus of the metallic wire, we can follow these steps:

### Step 1: Calculate the fundamental frequency of the organ pipe.
The fundamental frequency \( f \) of an open organ pipe is given by the formula:
\[ f = \frac{v}{\lambda} \]
where \( v \) is the speed of sound in air and \( \lambda \) is the wavelength.
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