General Wave Properties

This lesson explains General Wave Properties for Cambridge IGCSE Physics 0625. It separates the Core requirements from the additional Supplement work for Extended candidates. Focus on the cause-and-effect explanation and the exact quantities being compared. After the example, use the related practice questions to check what you can do independently.

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 example

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)

Original marking points:

• 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: $3.0\ \text{m/s}$

These marking points belong to this original example. They are not an official Cambridge mark scheme.

Common errors and how to correct them

• 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.

How to apply this in an exam

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.

Where this skill matters

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.