Wave Speed, Frequency and Wavelength

All waves transfer energy from one place to another without transferring matter. The three key quantities that describe a wave are speed, frequency and wavelength.

Definitions

Quantity	Definition	Unit
Wavelength ($\lambda$)	The distance between two consecutive points in phase (e.g. crest to crest)	m
Frequency ($f$)	The number of complete waves passing a point per second	Hz
Wave speed ($v$)	The distance travelled by the wave per second	m/s

The wave equation

$v = f\lambda$

This applies to all waves: mechanical (sound, water) and electromagnetic (light, radio).

Worked example

A sound wave has a frequency of 500 Hz and a wavelength of 0.66 m. Calculate the wave speed.

$v = f\lambda = 500 \times 0.66 = 330\text{ m/s}$

Worked example: finding wavelength

Radio waves travel at $3.0 \times 10^8$ m/s. A station broadcasts at a frequency of $9.0 \times 10^7$ Hz. Find the wavelength.

$\lambda = \frac{v}{f} = \frac{3.0 \times 10^8}{9.0 \times 10^7} = 3.3\text{ m}$

Common errors and how to correct them

Using kHz without converting to Hz. 1 kHz = 1000 Hz. Convert before substituting into $v = f\lambda$.

Confusing wavelength with amplitude. Wavelength is the horizontal distance between identical points on consecutive waves. Amplitude is the maximum vertical displacement from the rest position.

How to apply this in an exam

State the equation, substitute with correct units (m, Hz, m/s), and show the calculation. For electromagnetic waves in a vacuum, use $v = 3.0 \times 10^8$ m/s.