Using dimensions method show that the speed of sound in a material medium of modulus of elasticity E and density `rho` is `v prop sqrt(E/(rho))`

Explanation

To show that the speed of sound \( v \) in a material medium with modulus of elasticity \( E \) and density \( \rho \) is proportional to \( \sqrt{\frac{E}{\rho}} \) using the dimensions method, we can follow these steps:

### Step 1: Define the relationship
Assume that the speed of sound \( v \) is proportional to the modulus of elasticity \( E \) and density \( \rho \):
\[ v \propto E^x \rho^y \]
where \( x \) and \( y \) are the powers to which \( E \) and \( \rho \) are raised, respectively.
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