Question

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


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Answer 1

Answer:

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)