The big idea: Drop a pebble in a pond and ripples race outward, yet a floating leaf only bobs up and down — the water stays put while the wave carries energy across it.
Describing a wave: Four numbers describe any wave: its wavelength, frequency, amplitude and speed.
There are two ways to draw a wave — look along it (distance) or watch one point over time.
- Wavelength (λ)
- the length of one full wave (e.g. crest to crest). Unit: metre (m).
- Amplitude (A)
- the maximum displacement from the middle (rest) position. Unit: metre (m).
- Period (T)
- the time for one full wave to pass a point. Unit: second (s).
- Frequency (f)
- the number of waves per second. Unit: hertz (Hz), where 1 Hz = 1 per second.
Animated graph
Watch the graph build step by step in study mode.
Animated graph
Watch the graph build step by step in study mode.
Two graphs, two readings: Read wavelength λ off a distance graph (the x-axis is in metres).
Read period T off a time graph (the x-axis is in seconds).
Both look like the same S-shape — always check the axis label to know which one you have.
The wave moves, the medium does not
Waves carry energy: The energy moves with the wave, not the medium. The power of a wave is the energy it delivers each second: the energy stored in one wavelength passes a point in one period T.
For a sea wave, the water's gravitational PE and its KE both travel with the wave.
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The wave speed, frequency and wavelength are tied together by the wave equation, which is given in the data booklet. Know any two and you can find the third.
- wave speed (m s⁻¹)
- frequency — waves per second (Hz)
- wavelength — length of one full wave (m)
Frequency and period are linked: Frequency and period are two views of the same thing: f = how many waves per second, T = how long one wave takes.
They are reciprocals — T = 1/f (also given in the data booklet). So if T = 0.50 s then f = 2.0 Hz.
- period — time for one full wave (s)
- frequency — waves per second (Hz)
The wave equation v = f λ. Cover the one you want: f and λ side by side → multiply (v = f λ); v above λ → divide (f = v ÷ λ).
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A sound wave in air has a frequency of 170 Hz and travels at 340 m s⁻¹. Find its wavelength.
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How this is tested — the wave equation is the workhorse of every wave question:
Paper 1A
- A quick MCQ — find one of v, f or λ from the other two (often for sound or light).
Paper 2
- Read the wavelength off a displacement-distance graph and the period off a displacement-time graph.
- Then find the speed with v = λ ÷ T.
The classic trap: Mixing up the two graphs — wavelength comes from a distance axis, period from a time axis.
Speed straight from λ and T: Since f = 1/T, the wave equation v = f λ can be written as v = λ ÷ T.
So if a question gives you the wavelength and the period, you don't need f as a separate step — just divide.
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Watch the graph build step by step in study mode.
- wave speed (m s⁻¹)
- wavelength — length of one full wave (m)
- period — time for one full wave (s)
A sound wave is shown on two graphs. Its displacement-distance graph shows one full wave spanning 0.80 m; its displacement-time graph shows one full cycle taking 2.0 ms. Find the speed of the wave.
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