## Sound 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.

*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)}**

## One Comment

weldone nice explaination