Using the method of dimension, derive an expression for the velocity of sound waves. assume that the velocitu depends on:
(i) modulus of the elasticity e of the medium
(ii) the density of the medium p take constant k=i

v = K √(E / ρ)

Explanation:

Modulus of elasticity has units of N/m², or kg/m/s².

Density has units of kg/m³.

Velocity has units of m/s.

If we divide modulus of elasticity by density, we can eliminate kg:

E / ρ = [kg/m/s²] / [kg/m³]

E / ρ = [m²/s²]

Taking the square root gets us units of velocity:

√(E / ρ) = [m/s]

Multiply by the constant K:

v = K √(E / ρ)

Explanation:

Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. The device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force. The model for this is the law of the lever.