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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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Respuesta :

MathPhys

Answer:

v = K āˆš(E / Ļ)

Explanation:

Modulus of elasticity has units of N/mĀ², or kg/m/sĀ².

Density has units of kg/mĀ³.

Velocity has units of m/s.

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

E / Ļ = [kg/m/sĀ²] / [kg/mĀ³]

E / Ļ = [mĀ²/sĀ²]

Taking the square root gets us units of velocity:

āˆš(E / Ļ) = [m/s]

Multiply by the constant K:

v = K āˆš(E / Ļ)

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