General Properties of Waves
Waves transfer energy from place to place without transferring matter. That one sentence is the foundation of the whole topic, and it is also the thing most often got wrong.
1. What a wave does
A wave transfers energy — and information — without transferring matter.
When a wave passes through water, the water does not travel with it. Each particle oscillates about a fixed position and stays roughly where it was. A floating duck bobs up and down; it is not carried to the shore.
The particles move; they do not travel. Two opposite errors were recorded here: saying that matter moves along with the wave, and saying that “only energy moves, the particles don’t move at all”. Both are wrong. The particles vibrate about a fixed point, and the energy moves along.
2. Transverse and longitudinal waves
This is the most-confused distinction in the topic — it accounted for more recorded errors than anything else on this page.
Transverse: the particles vibrate at 90° (perpendicular) to the direction the wave travels. Longitudinal: the particles vibrate parallel to (along) the direction the wave travels.
| Transverse | Longitudinal | |
|---|---|---|
| Particle vibration | perpendicular to travel | parallel to travel |
| Features | crests and troughs | compressions and rarefactions |
| Examples | light, all EM waves, water waves, waves on a rope | sound, ultrasound, a pushed slinky |
| Needs a medium? | EM waves: no | yes, always |
Say what is perpendicular to what. “Transverse waves are perpendicular” scores nothing — perpendicular to what? The mark is for “the particles vibrate perpendicular to the direction of energy transfer”. This exact incompleteness was recorded, and it is the difference between one mark and none.
Sound is a LONGITUDINAL wave, not transverse. Saying sound is transverse was a direct error in lessons and is heavily examined.
Light is transverse; sound is longitudinal. If you remember only one pair, remember this one.
Compressions and rarefactions: in a longitudinal wave, a compression is where particles are squeezed together (high pressure) and a rarefaction is where they are spread apart (low pressure).
For a longitudinal wave, the wavelength is measured from one compression to the NEXT compression — centre to centre. Measuring within a single compression was a recorded error.
3. The key quantities
| Quantity | Symbol | Definition | Unit |
|---|---|---|---|
| Wavelength | λ (lambda) | distance between two corresponding points on adjacent waves | m |
| Amplitude | a | maximum distance from the undisturbed (rest) position | m |
| Frequency | f | number of complete waves per second | Hz |
| Period | T | time for one complete wave | s |
| Wave speed | v | distance travelled per second | m/s |
Amplitude is measured from the REST POSITION to the peak — not from trough to crest. A specific recorded error was defining amplitude as “the total distance between maximum and minimum displacement”, which is twice the amplitude. If a question gives you the peak-to-trough distance, halve it.
Wavelength is crest-to-crest, or trough-to-trough — any two matching points on consecutive waves. Reading it from a crest to the next trough gives half a wavelength.
Frequency is measured in hertz (Hz) — 1 Hz is one wave per second. Forgetting the unit was recorded; so was failing to convert kHz to Hz (× 1000) and MHz to Hz (× 1 000 000).
4. The two equations
v = f λ (speed = frequency × wavelength) T = 1/f and f = 1/T
Example: a wave has frequency 5 Hz and wavelength 3 m.
- v = 5 × 3 = 15 m/s
Example: a wave has period 0.25 s.
- f = 1/0.25 = 4 Hz
Period and frequency are reciprocals — divide, don’t multiply. Getting 0.5 Hz where 4 Hz was correct came from mishandling this. If T = 0.25 s, then four complete waves fit into each second.
To find wavelength, DIVIDE speed by frequency (λ = v/f). Multiplying instead was a recorded error and gives an answer wrong by a large factor.
Frequency never comes out negative. If it does, you have inverted something.
Rearranging safely: v = fλ gives f = v/λ and λ = v/f. Write the base equation down first, every time.
5. Frequency, wavelength and speed — what changes when
This is the conceptual heart of the topic, and it is examined constantly.
In a given medium, v = fλ means frequency and wavelength are INVERSELY proportional — a higher frequency means a shorter wavelength, at constant speed.
But when a wave crosses into a new medium (refraction):
The FREQUENCY stays the same. The SPEED changes, and so the WAVELENGTH changes.
Frequency is set by the source, so it cannot change en route. When light enters water it slows down, so from v = fλ the wavelength decreases.
Saying “the wavelength stays the same when light enters water” is wrong, and so is “the speed stays the same when the wavelength decreases” — both were recorded. The rule: frequency fixed, speed changes, wavelength follows.
Speed of sound varies with the medium — fastest in solids, slower in liquids, slowest in gases, because the particles are closer together and pass the vibration on more quickly:
- air ≈ 330–340 m/s
- water ≈ 1500 m/s
- steel ≈ 5000 m/s
Sound travels perfectly well through water — saying otherwise was a recorded error. What sound cannot do is travel through a vacuum, because there are no particles to vibrate.
A vacuum is not air. Confusing the two was recorded. Light can cross a vacuum; sound cannot.
This is a two-mark answer. As one tutor put it: one mark for saying sound cannot travel through a vacuum, one for explaining that there are no particles to transmit the vibrations. State both.
6. Wavefronts and wave behaviour
A wavefront is a line joining points on the wave that are in phase — usually drawn along the crests. The distance between adjacent wavefronts is the wavelength, and the wave travels perpendicular to the wavefronts.
Reflection
The wave bounces off a barrier. The angle of incidence = angle of reflection, both measured from the normal. Speed, frequency and wavelength all stay the same.
Refraction
The wave changes speed on entering a new medium, and therefore changes direction (unless it enters along the normal).
- Entering a slower medium (e.g. shallower water, or glass): bends towards the normal, wavelength decreases
- Entering a faster medium: bends away from the normal, wavelength increases
Water waves travel more slowly in shallow water. Getting this backwards was recorded — the shallow region is the “slow” medium, so wavefronts bunch closer together and bend towards the normal.
Diffraction
Diffraction is the spreading out of a wave as it passes through a gap or around an edge.
The amount of spreading depends on the gap size compared with the wavelength:
The closer the gap width is to the wavelength, the MORE the wave spreads out.
- Gap much wider than λ: little diffraction, wave passes almost straight through
- Gap similar to λ: maximum diffraction, waves spread out in semicircles
In diffraction, wavelength, frequency and speed are all unchanged — only the shape of the wavefronts changes.
Wavefronts approaching a gap are straight (plane); after a narrow gap they become curved. Misdrawing the incoming wavefronts as curved was a recorded error — the curvature appears after the gap.
Longer wavelengths diffract more. This is why radio waves bend around hills but light does not, and why you can hear round a corner but not see round it.
7. Mistakes that cost marks
Saying a wave transfers matter.
Saying transverse/longitudinal waves are “perpendicular/parallel” without stating to what.
Saying sound is a transverse wave.
Defining amplitude as peak-to-trough.
Measuring wavelength from crest to trough, or within a compression.
Forgetting the unit Hz, or not converting kHz and MHz.
Multiplying when finding wavelength instead of dividing.
Confusing period with frequency.
Saying frequency changes during refraction. It doesn’t.
Saying wavelength stays the same when light enters glass or water.
Saying sound can’t travel through water, or that it can travel through a vacuum.
Saying speed doesn’t change when wavelength changes on entering a new medium.
Not converting units before using v = fλ.
Frequently asked questions
What do waves transfer? Energy (and information) — not matter.
What is the difference between transverse and longitudinal waves? In transverse waves the particles vibrate perpendicular to the direction of energy transfer; in longitudinal waves they vibrate parallel to it.
Is sound transverse or longitudinal? Longitudinal. Light is transverse.
What is amplitude? The maximum distance from the rest position — half the peak-to-trough distance.
What is the wave equation? v = f λ.
What is the relationship between frequency and period? f = 1/T — they are reciprocals.
What happens to a wave when it refracts? The speed and wavelength change; the frequency stays the same.
Why can’t sound travel through a vacuum? There are no particles to vibrate and pass the energy on.
In which medium does sound travel fastest? Solids, because the particles are closest together.
What is diffraction? The spreading of a wave through a gap or around an edge — greatest when the gap is about the same size as the wavelength.
Quick revision checklist
- I know waves transfer energy, not matter
- I can define transverse and longitudinal relative to the direction of travel
- I know sound is longitudinal and light is transverse
- I can identify compressions and rarefactions
- I measure wavelength between corresponding points
- I know amplitude is measured from the rest position
- I know the units of frequency and can convert kHz and MHz
- I can use v = fλ and rearrange it correctly
- I can use f = 1/T
- I know frequency is fixed by the source and doesn’t change on refraction
- I know speed and wavelength change together in a new medium
- I know why sound can’t cross a vacuum, and can explain it
- I know the order of sound speeds in solids, liquids and gases
- I can describe reflection, refraction and diffraction of wavefronts
- I know diffraction is greatest when the gap ≈ the wavelength
These notes cover the general properties of waves in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons — this was the most-taught topic in that set — with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
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