General Wave Properties

The key wave quantities are wavelength, frequency, amplitude and wave speed, linked by $v = f\lambda$. Every wave question in IGCSE Physics 0625 (light, sound, the electromagnetic spectrum) builds on the definitions and that one equation. Examiners test it directly every session because $v = f\lambda$ is among the most-used equations on the paper.

What are the key wave quantities and the wave equation?

A wave transfers energy without transferring matter. That definition is worth a mark on its own and rules out the classic wrong answer that “water moves along with the wave”.

Quantity	Symbol	Unit	Meaning
Wavelength	$\lambda$	metre (m)	Distance between two adjacent crests (or any two matching points)
Frequency	$f$	hertz (Hz)	Number of waves passing a point per second
Amplitude	$A$	metre (m)	Maximum displacement from the rest position
Wave speed	$v$	m/s	Distance travelled by a wavefront per second

The wave equation in words: $\text{wave speed} = \text{frequency} \times \text{wavelength}$. In symbols: $v = f\lambda$. A wavefront is a line joining points moving in step, like the crest lines spreading from a stone dropped in water. Time period $T$ is the time for one complete wave, where $T = \dfrac{1}{f}$.

How do you read amplitude and wavelength from a diagram?

Amplitude is measured from the centre (rest) line to a crest, never from crest to trough. Crest-to-trough is twice the amplitude. Wavelength is measured crest to crest, or between any two identical points one full cycle apart. On a displacement-time graph the horizontal axis gives the period, not the wavelength; on a displacement-distance graph it gives the wavelength. Check the axis label before answering, because this distinction catches out a large share of candidates.

Worked Exam Question

Water waves in a harbour have a wavelength of 2.5 m. A buoy bobs up and down 12 times in 10 seconds. Calculate (a) the frequency of the waves and (b) their speed. [4]

Worked solution:

1. (a) Frequency = waves per second $= 12 \div 10 = 1.2\ \text{Hz}$
2. (b) Equation: $v = f\lambda$
3. Substitute: $v = 1.2 \times 2.5$
4. Answer: $v = 3.0\ \text{m/s}$ (2 significant figures)

Mark scheme:

• M1: $12 \div 10$
• A1: $f = 1.2\ \text{Hz}$ (unit required)
• M1: $v = f\lambda$ with correct substitution (error carried forward from (a) allowed)
• A1: $3.0\ \text{m/s}$

Common Mistakes

• Measuring amplitude from crest to trough. Halve it: amplitude runs from the rest position to the crest.
• Leaving wavelength in centimetres when speed is needed in m/s. Convert before substituting: $50\ \text{cm} = 0.50\ \text{m}$.
• Confusing frequency with speed. Frequency counts waves per second; speed measures how far a crest travels per second.
• Writing $T = f$ instead of $T = \dfrac{1}{f}$. Period and frequency are reciprocals.
• Saying the medium travels with the wave. The water (or air) oscillates about a fixed point; only energy moves along.

Exam Technique Tip

When a question gives a diagram, write $\lambda$ and the amplitude on the diagram itself before calculating. Annotating forces you to read values correctly and shows the examiner your method. Then follow the fixed routine: equation in symbols, substitute with units converted, rearrange if needed, answer with unit and sensible significant figures.

How This Is Examined

This subtopic appears on all papers. Papers 1 and 2 give a labelled wave diagram and ask for amplitude, wavelength or a one-step $v = f\lambda$ calculation. Papers 3 and 4 combine the calculation with definitions; Extended (Paper 4) versions add rearrangement for $f$ or $\lambda$ and unit conversions involving kHz or MHz, especially in electromagnetic-spectrum contexts. Papers 5 and 6 can ask you to measure wavelength from a scale diagram or plot wave data on a graph. One equation does carry this subtopic. Across a typical session, $v = f\lambda$ and its rearrangements appear at least three times across the paper set.