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# Wave representation

## Wave representation

Waves (both transverse and longitudinal) are typically represented as a graph where:

• The x-axis represents the position of the oscillation along the wave's direction of motion (or along the length of the wave) at a specific point in time (the shape of the graph varies with time).
• The y-axis represents the oscillating physical quantity (e.g. oscillatory displacement of particles, magnetic field, electric field).

A mechanical wave can be represented as a graph of displacement (i.e. oscillatory displacement) vs position.

It is important not to confuse the terms "position" and "displacement" in the context of waves.

• "Displacement" refers to the oscillatory movement of a particle from its equilibrium position and not the displacement of an entire wave from its point of origin.
• "Position" refers to the location of a particle along the direction of motion of a wave (i.e. along a particular axis) and not its position in the oscillatory motion.

## Representing longitudinal waves

Longitudinal waves are sometimes represented as a series of lines corresponding to the positions of the particles of the wave along a single axis (typically the x-axis).

This representation is a more accurate description of a longitudinal wave (as both oscillatory and overall wave movement occurs in a single direction).

A simple longitudinal wave is a series of compressions (contractions) and rarefactions (expansions) of a physical medium.

This series corresponds to the crests (maximum points) and troughs (minimum points) of a sinusoidal transverse wave.

The lines which are close together represent a compression, while lines spaced far apart represent a rarefaction.

Longitudinal (above) and transverse (below) wave comparisons. The C's and R's represent the locations of compressions and rarefactions