The big idea: A wave carries energy from place to place without the material itself travelling along.
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.
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 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)
[Diagram: phys-formula-triangle] - Available in full study mode
Worked example — find the wavelength
A sound wave in air has a frequency of 170 Hz and travels at 340 m s⁻¹. Find its wavelength.
Solution
- Start with the given wave equation:
- Rearrange to make λ the subject:
- Put in the numbers (v = 340, f = 170):
- Work it out — keep the unit:
Final answer
wavelength λ = 2.0 m.
See how examiners mark answers
Access past paper questions with model answers. Learn exactly what earns marks and what doesn't.
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.
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.
- wave speed (m s⁻¹)
- wavelength — length of one full wave (m)
- period — time for one full wave (s)
IB-style question — speed of a sound wave from graphs
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.
Solution
- Read the wavelength off the distance graph:
- Read the period off the time graph (2.0 ms = 2.0 × 10⁻³ s):
- Use the given wave equation with the period:
- Put in the numbers:
- Work it out — keep the unit:
Final answer
speed v = 400 m s⁻¹.