The Wave Equation

Waves transfer energy without moving matter from place to place. The wave equation links three key ideas so you can calculate wave speed, frequency, or wavelength.

Key ideas

• Wave speed (v): how fast the wave pattern moves, in metres per second (m/s).
• Frequency (f): how many waves pass a point each second, in hertz (Hz). 1 Hz means “one per second”.
• Wavelength (λ): the distance between two matching points on a wave (crest to crest), in metres (m).
• Period (T): time for one wave to pass. It links to frequency by $T = \frac{1}{f}$.

The equation

The three quantities are connected by:

$$v = f\,\lambda$$

If a wave changes medium (for example, light entering glass), its speed and wavelength change, but its frequency stays the same. For electromagnetic waves in a vacuum, the speed is $c = 3.0\times10^{8}\,\text{m/s}$.

Common mistakes to avoid

• Mixing units (e.g., using cm with m). Always convert first.
• Thinking amplitude affects speed. Speed depends on the medium, not on amplitude.
• Assuming wavelength grows with frequency. For fixed speed, if $f$ increases, $\lambda$ decreases.
• Changing frequency at a boundary. Frequency stays the same when a wave enters a new medium; speed and wavelength change.