# Wave characteristics review

Review the characteristics of periodic transverse and longitudinal waves such as wavelength, crest, trough, amplitude, expansion, and compression.

## Key terms

Term (symbol)Meaning
Wavelength ($\lambda$)Distance between adjacent maxima or minima of a wave.
Periodic waveWave that repeats over time and space. Also called a continuous wave.
CrestHighest point on a transverse wave. Also called the peak.
TroughLowest point on a transverse wave.
ExpansionA point of maximum spacing between particles of a medium for longitudinal waves.
CompressionA point of minimum spacing between particles of a medium for longitudinal waves.

## Equations

EquationSymbolsMeaning in words
$\lambda = \dfrac{v}{f}$$\lambda$ is wavelength, $v$ is wave speed, and $f$ is frequencyWavelength is wave speed divided by frequency.

## How to identify parts of a wave

### Transverse waves

Transverse waves vibrate the particles of a medium perpendicularly to the direction of wave travel to produce the features shown in Figure 1 below.
Figure 1: Parts of a transverse wave.

### Longitudinal waves

Longitudinal waves form when the particles of the medium vibrate back and forth in the same direction of the traveling wave. The wave can be visualized as compressions and expansions travelling along the medium. The distance between adjacent compressions is the wavelength.
Figure 2: Parts of a longitudinal wave.

## How to understand the wave speed equation

The speed $v$ of a wave is constant for any unchanging medium, so frequency and wavelength are inversely proportional. The wave speed equation is not a new equation, it’s just a different way of writing
$v = \dfrac{\Delta x}{t}$
which we can rearrange to get
$\Delta x = vt$
Wavelength $\lambda$ is the distance that a wave crest (or trough) travels over one period $T$. We can write period in terms of frequency $f$. Let’s make these substitutions to get:
\begin{aligned}\lambda &= vT \\ \\\\ \lambda&=\dfrac{v}{f}\end{aligned}

## How waves transport energy

Waves carry energy through a medium. Any displacement of the wave is resisted by a directly proportional restoring force. The work to produce a big wave amplitude requires both large forces and displacements, which results in more wave energy.
Therefore, energy transported by a wave increases with the wave amplitude.

## Common mistakes and misconceptions

Sometimes people forget that the wave speed stays the same unless the properties of a medium change. Therefore, changing frequency will change the wavelength, and vice versa. For example, transverse waves on a string travel more quickly with increased tension.