A metal wire with volume density `rho` and young's modulus `Y` is stretched between rigid supports. At temperature `T`, the speed of a transverse wave is found to be `v_(1)`. When temperature decreases `T - DeltaT`, the speed increases to `v_(2)`. Datermine coefficient of linear expansion of wire.

Explanation

To determine the coefficient of linear expansion of the wire, we will follow these steps:

### Step 1: Understand the relationship between wave speed, tension, and mass density
The speed of a transverse wave in a wire is given by the formula:
\[ v = \sqrt{\frac{F}{\mu}} \]
where \( F \) is the tension in the wire and \( \mu \) is the mass per unit length (linear density) of the wire, defined as:
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