what is the relationship between speed of sound in a medium , elastic constant, density of a medium
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Speed of sound =√(modulus of elasticity)/√(density)
khus14:
how will u express it in terms of dimensional analysis
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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)
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