Progressive Wave and Its Equation | Physics Grade XII

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Progressive Wave Equation-1Sound and Waves | Physics
Progressive Wave and Its Equation
For: Science Class 12

A wave in which crest – trough transverse wave and compression and rarefaction in longitudinal wave is called progressive wave. The amplitude of each particle is same and energy is transferred forward along the wave.

Progressive Wave Equation

Fig: Progressive Wave

Suppose, a transverse moves from left to right in which each particles vibrates simple harmonically. The displacement y of the vibrating particle at origin O is

y = a.sinωt —– (i)
Where, a is an amplitude.

Suppose, a particle which is at point p lies at a distance x from the origin. Suppose Ø be the phase angle lags of the particles p, λ be the wave length of the wave.

The displacement of a particle at point p at a distance x from the origin is given by:

Y = a.sin(ωt – Ø) —- (ii)

Where, Ø be the phase angle.

Or, y = a.sine{ωt – (2πx / λ)
Or, y = a.sine{ωt – (kx) — (iii)

Where k = (2πx / λ) which is known as wave number.

Or, y = a.sine{2π(t / T) – (2πx / λ)}
Or, y = a.sine2π{(t / T) – (x / λ)} — (iv)

Equation (iii) and (iv) are known as progressive wave equation.
If the particles of the wave move from right to left then, Or, y = a.sine2π{(t / T) + (x / λ)}

Posted By : MeroSpark | Comment RSS | Category : Class XII, HSEB Notes
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One Comment

  1. Posted January 3, 2017 at 1:50 am

    weldone nice explaination

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