Displacement Relation in a Progressive Wave

Displacement Relation in a Progressive Wave

Progressive Wave:

A wave that travels from one point of the medium to another is called a progressive wave. A progressive wave may be transverse or longitudinal.

Plane progressive harmonic wave:

If during the propagation of a wave through a medium, the particles of the medium vibrate simply harmonically about their mean positions, then the wave is said to be a plane progressive harmonic wave.

Displacement relation for a progressive harmonic wave:

The displacement in a sinusoidal wave propagating in the positive x-direction is given by

where a is the amplitude of the wave, k is the angular wave number, ω is the angular frequency, (kx – ωt + φ) is the phase, and φ is the phase constant or phase angle.

The sine function and the time-dependent phase of a wave correspond to the oscillation of a string element, and the amplitude of the wave determines the extremes of the element’s displacement. The constant ϕ is called the initial phase angle.


Wavelength λ of a progressive wave is the distance between two consecutive points of the same phase at a given time. In a stationary wave, it is twice the distance between two consecutive nodes or antinodes. k is called the propagation constant or the angular wave number.

Its SI unit is radian per meter or rad m-1.

Period and Frequency:

Period T of oscillation of a wave is defined as the time any element of the medium takes to move through one complete oscillation. It is related to the angular frequency ω through the relation

Frequency v of a wave is defined as 1/T and is related to angular frequency by

It is the number of oscillations per unit time made by a string element as the wave passes through it. It is usually measured in Hertz.

How useful was this post?

Click on a star to rate it!

Average rating / 5. Vote count:

As you found this post useful...

Follow us on social media!

We are sorry that this post was not useful for you!

Let us improve this post!


Please enter your comment!
Please enter your name here