# What is the relationship between speed of sound in a medium , elastic constant, density of a medium

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by khus14

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by khus14

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Speed of sound =√(modulus of elasticity)/√(density)

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Speed = v = [ L ] [ T⁻¹ ]

volume density = d = [ M ] [ L⁻³ ]

Young's Modulus in a solid = [ M ] [ L⁻¹ ] [ T⁻² ]

v = k Y^a d^b

[ L ] [ T⁻¹ ] = [ M ]^a [ L⁻¹ ]^a [ T⁻² ]^a [ M ]^b [ L⁻³ ]^b

compare the powers of M, L, and T respectively on both sides.

a + b = 0

-a -3b = 1 => -2b = 1 => b = -1/2 a = 1/2

Hence v = √(Y/d)

volume density = d = [ M ] [ L⁻³ ]

Young's Modulus in a solid = [ M ] [ L⁻¹ ] [ T⁻² ]

v = k Y^a d^b

[ L ] [ T⁻¹ ] = [ M ]^a [ L⁻¹ ]^a [ T⁻² ]^a [ M ]^b [ L⁻³ ]^b

compare the powers of M, L, and T respectively on both sides.

a + b = 0

-a -3b = 1 => -2b = 1 => b = -1/2 a = 1/2

Hence v = √(Y/d)