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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.

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