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Mechanical Wave (Notes)

Mechanical Wave

Mechanical Wave:

The wave which requires a material medium for its propagation is called a mechanical wave. e.g. sound wave is a longitudinal mechanical wave.

When a longitudinal wave propagates in a medium, slight increase in pressure takes place at the region of compression and slight decrease in pressure takes place at the region of rarefaction, i.e. variation in pressure takes place in the medium during the propagation of longitudinal wave. So, it is also called a pressure wave.

Velocity of Sound:

Dimensional method:

Experimentally it has been found that the velocity of sound din a medium depends upon the value of modulus of elasticity (E) and density (ρ) of medium.

Let V ∝ Ex and V ∝ ρy, where x and y are the power to be determined.

Combining above relations we get,
V ∝ Ex ρy

or, V = kEx ρy          ........(i), where k is dimensionless constant.

Replacing the physical quantities in above equation by their dimensional formulae we get,
[M0LT-1] = [ML-1T-2]y [ML-3]y
or, [M0LT-1 = [Mx+yL-x-3yT-2x]

Eqating the powers on both sides we get,
-2x = -1 ⇒ x = 1/2

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