A wave is a repeating disturbance. To talk about one precisely, you need the five words that physicists use: wavelength, frequency, period, amplitude, and the two reference points where everything begins. Crest and trough.
The Key Idea
Every wave in the syllabus, water ripples, sound, light, microwaves, is described by exactly the same five quantities. Learn them once on a water wave, and the language transfers to every other wave you will ever meet.
SECTION 01
The five features.
Imagine you are looking sideways at a wave on the surface of a tank of water. You take a photograph. That snapshot, frozen in time, shows you four of the five features at once. The fifth, frequency, hides until you start a stopwatch.
A frozen snapshot of a wave shows wavelength, amplitude, crest, and trough. Frequency lives in time.
Wavelength
symbol λ · unit metres (m)
The distance from one point on the wave to the next identical point. Easiest to measure crest to crest, or trough to trough.
Amplitude
symbol a · unit metres (m)
The maximum distance any point on the wave moves from its rest position. Not the full crest-to-trough height, just half of it.
Frequency
symbol f · unit hertz (Hz)
The number of complete waves that pass a fixed point per second. A 50 Hz wave produces 50 crests every second.
Period
symbol T · unit seconds (s)
The time for one complete wave to pass. The reciprocal of frequency: T = 1 ÷ f. A 50 Hz wave has a period of 0.02 s.
Crest
highest point
The top of the wave, where the disturbance reaches its maximum positive value.
Trough
lowest point
The bottom of the wave, where the disturbance reaches its maximum negative value.
SECTION 02
The two graphs.
This is where students lose marks in the exam. There are two graphs that can describe a wave, and they look almost identical. The difference is on the x-axis.
Displacement against distance. A snapshot in space. The x-axis is distance along the wave. You can read the wavelength off this graph (one full wave, crest to crest).
Displacement against time. A snapshot in time at one location. The x-axis is time. You can read the period off this graph (one full cycle from start to start). From the period, you get frequency: f = 1 ÷ T.
Both graphs show the same amplitude. Both graphs show crests and troughs. But only the distance graph shows wavelength, and only the time graph shows period. Check the x-axis before you read anything.
Worked Example
A water wave is described by a displacement-time graph. The graph shows that one complete wave takes 0.4 seconds, and the amplitude is 0.02 m. Find the frequency of the wave.
Step 1 · Identify what you know
Period T = 0.4 s. Amplitude a = 0.02 m. The amplitude is irrelevant here, included to test whether you spot it.
Step 2 · Apply the relationship
f = 1 ÷ T
Step 3 · Substitute and solve
f = 1 ÷ 0.4 = 2.5 Hz
The wave has a frequency of 2.5 Hz. Two and a half complete waves pass any point each second.