scienceGrade 9-102 min read

Waves: the properties, and the one equation

Every wave — sound, light, water — shares the same handful of properties and a single equation linking them. Plus the difference between transverse and longitudinal that examiners love.

A wave is a way of moving energy from one place to another without moving matter along with it. A cork on a pond bobs up and down as the wave passes; it doesn't travel across the pond. Hold on to that — it's the idea behind half the exam questions.

The properties

Property	Symbol	Meaning
Wavelength	$\lambda$	Length of one full wave (metres)
Frequency	$f$	Waves passing per second (hertz, Hz)
Amplitude	$A$	Height from the middle to a peak
Period	$T$	Time for one full wave (seconds)
Speed	$v$	How fast the wave travels (m/s)

Amplitude is the wave's "size" — for sound it's loudness, for light it's brightness. It is not the same as wavelength, and mixing them up is the classic error.

The wave equation

The one relationship that links speed, frequency, and wavelength:

v = f\lambda

If you know any two, you can find the third. And since period is just "time for one wave," frequency and period are reciprocals:

f = \frac{1}{T}

Transverse vs longitudinal

Transverse: the wobble is at right angles to the direction of travel — like shaking a rope, or light, or water waves. Peaks and troughs.
Longitudinal: the wobble is along the direction of travel — like sound, which travels as squashes and stretches (compressions and rarefactions) in the air.

Worked example

A sound wave has frequency $170\,\text{Hz}$ and wavelength $2\,\text{m}$ . Its speed:

v = f\lambda = 170 \times 2 = 340\ \text{m/s}

— which is, reassuringly, the speed of sound in air.

Check your units feed the equation. Frequency in hertz and wavelength in metres give speed in m/s. If a wavelength is quoted in centimetres, convert it first — a missed conversion turns a right method into a wrong answer.

Last revised 10 June 2025.