Equations of Wave Motion

Waves can be described by the motion and position of the particles of the medium through which they move.

If we graph the vertical height of the wave to its position, we see that every particle in the medium oscillates up and down in a simple harmonic motion with the same frequency.

The equilibrium position of the wave is along a straight line and considered to be the x-axis of a coordinate system.

Consider a particle of the medium in which the wave moves. It displaces from the equilibrium position to a certain height in the positive and negative direction of the y-axis in a period T. The wave motion is sinusoidal and is translating in the positive x-direction as time progresses.

The value of particle displacement from the equilibrium position is a function of both position and time and is known as a wave function.

The plus and minus signs indicate whether the wave moves in the negative or positive x-direction, respectively.