What is the difference between transverse and longitudinal waves?

In a transverse wave the particles oscillate at right angles to the direction the energy travels (a wave on a rope). In a longitudinal wave they oscillate parallel to it, making compressions and rarefactions (sound). Both carry energy without carrying the medium along.

What is the difference between a displacement–time graph and a displacement–distance graph?

A displacement–distance graph is a snapshot of the whole wave at one instant: crest to crest is the wavelength. A displacement–time graph follows one particle over time: crest to crest is the period. Check the horizontal axis to tell them apart.

Is amplitude measured from crest to trough?

No. Amplitude is the maximum displacement from the rest position, so it is measured from the middle line to a crest. Crest to trough is twice the amplitude.

Does the frequency of a wave change when it enters a new medium?

No. The frequency is set by the source. The speed changes in the new medium, so the wavelength changes too (λ = v/f). This is what happens in refraction.

As a sound wave travels through air, how do the air particles move?

They oscillate parallel to the direction the energy travels.

They oscillate at right angles to the direction the energy travels.

They travel along with the wave at the speed of sound.

They stay completely still while the energy passes.

The frequency of a wave on a string is doubled, with the tension unchanged. What happens?

The speed stays the same and the wavelength halves.

The speed doubles and the wavelength stays the same.

The speed stays the same and the wavelength doubles.

The speed and the wavelength both double.

Year 11 Physics · Waves · Wave properties · 11 min read

Wave properties

A wave carries energy from one place to another without carrying the material along with it. A ripple crosses a pond, but the water just bobs up and down; a sound reaches your ear, but the air near the speaker stays where it is.

This guide covers the two kinds of mechanical wave, the parts of a wave (amplitude, wavelength, period and frequency), the wave equation v = fλ, and the two wave graphs that look the same but aren't. Then there is a quick quiz and a full worked example.

What you need to know

Model particle oscillation in longitudinal and transverse waves by conducting a practical investigation, relating it to the direction energy travels.
For transverse waves, describe amplitude, crest, trough, wavelength, period and frequency.
For longitudinal waves, describe amplitude, compression, rarefaction, wavelength, period and frequency.
Use f = 1/T and v = fλ to solve problems.
For transverse and longitudinal waves, analyse displacement–time graphs.
For transverse and longitudinal waves, analyse displacement–distance graphs.

The equations you will use:

f = 1/TFrequency in hertz (Hz = s⁻¹) from the period in seconds. It works the other way too: T = 1/f.

v = fλWave speed (m s⁻¹) = frequency (Hz) × wavelength (m). Equivalent to v = λ/T.

Dot points: PY11-WV-01, PY11-WV-02, PY11-WV-03, PY11-WV-04, PY11-WV-05, PY11-WV-06 (2025 Physics syllabus, Year 11), in our own words.

Mini lesson

Energy moves, the medium doesn't

A mechanical wave is a disturbance passed from particle to particle through a medium (a rope, water, air). Each particle oscillates about its own rest position and ends up where it started. It's the energy that travels.

Transverse: the particles oscillate at right angles to the direction the energy travels. Example: a wave on a rope or a guitar string.
Longitudinal: the particles oscillate parallel to the direction the energy travels, making compressions (particles bunched together) and rarefactions (particles spread out). Example: sound.
In the practical, a slinky does both: flick one end sideways for a transverse wave, push it in and out for a longitudinal one. A ribbon tied to one coil only moves back and forth while the pulse runs the whole length.

Transverse: particles move at right angles to the energy's direction. Longitudinal: particles move back and forth along it, forming compressions (C) and rarefactions (R).

The parts of a wave

Crest and trough: the highest and lowest points of a transverse wave.
Amplitude (A): the maximum displacement from the rest position, so from the middle line to a crest. It is not crest to trough.
Wavelength (λ): the distance between two neighbouring points in the same phase, such as crest to crest, in metres. For a longitudinal wave it is compression to compression (or rarefaction to rarefaction).
Period (T): the time for one complete oscillation of a particle, which is also the time for one whole wavelength to pass a point, in seconds.
Frequency (f): the number of oscillations per second, in hertz (Hz). f = 1/T.
For a longitudinal wave, the amplitude is the furthest a particle moves from its rest position along the line of travel.

The x-axis is the rest position. Amplitude A runs from the rest line to a crest or trough; wavelength λ runs from a crest to the next crest.

The wave equation: v = fλ

In one period, a wave moves forward exactly one wavelength. So its speed is v = λ/T, and since f = 1/T, v = fλ.

The source sets the frequency. Shake a rope faster and f goes up.
The medium sets the speed. For the same rope at the same tension, or air at the same temperature, v stays the same.
So in one medium, a higher frequency means a shorter wavelength: double f and λ halves.
Convert first: ms to s, cm to m, kHz to Hz. A wave with T = 4.0 ms has f = 1 ÷ 0.0040 = 250 Hz.

Two graphs that look the same

Wave questions use two graphs that look alike but mean different things. Always read the horizontal axis first.

Displacement–distance graph: a snapshot of the whole wave at one instant. The x-axis is position (m), so crest to crest is the wavelength.
Displacement–time graph: the motion of one particle over time. The x-axis is time (s), so crest to crest is the period, and f = 1/T.
The amplitude is read off the vertical axis in both, from zero to a peak.
Put them together: λ from the distance graph, T from the time graph, and v = λ/T.

Same shape, different meaning. On a distance axis, crest to crest is λ (in m); on a time axis, it is T (in s).

To find which way a particle on a snapshot is moving, picture the wave shifted a little in its direction of travel. If the curve at that particle's position is now higher, the particle is moving up; if lower, it is moving down.

Longitudinal waves on a displacement graph

A sound wave can be drawn on the same axes, but now the displacement is along the direction of travel. Take positive to mean a particle has moved forward (the way the wave is going) and negative to mean it has moved back.

At a compression, the particles just behind have moved forward and the particles just ahead have moved back, so they crowd together: the graph crosses zero going from positive to negative. At a rarefaction, the graph crosses zero going from negative to positive. The peaks are not compressions; they are where particles have moved furthest forward.

Compression to compression is still one wavelength, and v = fλ works in exactly the same way.

s is each particle's displacement along the line of travel (+ = moved forward, the way the wave travels: to the right here). Compressions (C) sit where the graph crosses zero going down; rarefactions (R) where it crosses going up.

Common mistakes

Measuring the amplitude from a crest to a trough.Amplitude is from the rest position to a crest (or to a trough): half the crest-to-trough height.
Reading the gap between crests on a displacement–time graph as the wavelength.On a time axis, crest to crest is the period. Check the axis label and unit (s or m) before reading anything.
Thinking the particles of the medium travel along with the wave.Each particle oscillates about its rest position. Energy is transferred; the medium is not.
Saying a higher frequency makes a wave travel faster.In one medium the speed stays the same. A higher frequency gives a shorter wavelength.
Labelling the peaks of a longitudinal wave's displacement graph as compressions.Compressions are where the particles on either side have moved towards that point. With + meaning moved in the direction of travel, that is where the graph crosses zero going from positive to negative.
Substituting T = 4.0 ms as 4.0 in f = 1/T and getting 0.25 Hz.Convert first: 4.0 ms = 0.0040 s, so f = 1 ÷ 0.0040 = 250 Hz.

Worked example

Waves travel across a lake towards a jetty. A buoy floating on the water moves from its highest point to its lowest point, a vertical distance of 0.60 m, in 1.25 s. A photo taken from a drone shows that the horizontal distance from a crest to the next trough is 3.0 m.

(a) State the amplitude of the waves. (1 mark)

(b) Calculate the frequency and the speed of the waves. (3 marks)

(5 marks)

I'll think out loud, the way you should in the exam, using KNOW-UD: Knowns, Not known, Organise, Work it out, Units, Direction.

Prediction first. Highest to lowest is half an oscillation, and crest to the next trough is half a wavelength, so I expect T ≈ 2.5 s and λ ≈ 6 m. That makes the speed a bit over 2 m s⁻¹, so 45 m should take roughly 20 s. The amplitude should be half of 0.60 m.

K · Knowns

I sketch the wave with the numbers on it. Both measurements are halves: high to low is half a period, and a crest to the next trough is half a wavelength. Writing that down stops me using them as whole ones.

crest-to-trough height = 0.60 m
highest → lowest: 1.25 s = ½T
crest → next trough: 3.0 m = ½λ
distance to the jetty: d = 45 m

Knowns on the sketch: crest-to-trough height 0.60 m, highest to lowest in 1.25 s (half a period), crest to next trough 3.0 m (half a wavelength), 45 m to the jetty. Not to scale.

N · Not known

There are four answers: the amplitude in metres, the frequency in hertz, the speed in m s⁻¹, and a time in seconds.

A = ? m, f = ? Hz, v = ? m s⁻¹, t = ? s

O · Organise

The amplitude is half the crest-to-trough height. T and λ are double the halves I was given. Then f = 1/T and v = fλ. A crest moves at the wave speed, so the travel time is distance ÷ speed.

A = ½ × (crest-to-trough height)
T = 2 × 1.25 s, λ = 2 × 3.0 m
f = 1/T, v = fλ, t = d ÷ v

W · Work it out

I go line by line and keep the full time value until the end.

A = ½ × 0.60 = 0.30 m
T = 2 × 1.25 = 2.5 s → f = 1 ÷ 2.5 = 0.40 Hz
λ = 2 × 3.0 = 6.0 m → v = fλ = 0.40 × 6.0 = 2.4 m s⁻¹
t = d ÷ v = 45 ÷ 2.4 = 18.75 s

U · Units

Metres, hertz, metres per second and seconds. The data have two significant figures, so I round the time to two.

A = 0.30 m, f = 0.40 Hz, v = 2.4 m s⁻¹, t ≈ 19 s

D · Direction

The waves move towards the jetty, so I say that with the speed. As a sense check I find the speed the other way, from v = λ/T, and it should agree.

v = 2.4 m s⁻¹ towards the jetty
check: λ/T = 6.0 ÷ 2.5 = 2.4 m s⁻¹, the same

(a) A = 0.30 m. (b) f = 0.40 Hz and v = 2.4 m s⁻¹. (c) About 19 s.

Check against the prediction. I predicted T ≈ 2.5 s and λ ≈ 6 m, a speed a bit over 2 m s⁻¹ and roughly 20 s to the jetty. 2.4 m s⁻¹ and 19 s fit.

Exam advice

What markers look for

Read the axis label and unit before you read any value off a wave graph. A time axis gives the period; a distance axis gives the wavelength.CortexHSC teaching notes
Convert to SI units before substituting: ms to s, cm to m, kHz to Hz. HSC markers flagged unconverted units (centimetres, millimetres, kilometres) in several 2024 questions, and wave questions are full of prefixes.NESA marking feedback, 2024, summarised
Use the graph or diagram you are given: quote the values you read from it ('crest to crest is 0.40 m') instead of writing a general answer. HSC feedback has flagged answers that ignored the stimulus.NESA marking feedback, 2025, summarised
Define terms exactly. 'Amplitude is the maximum displacement from the rest position' earns the mark; 'the height of the wave' doesn't.CortexHSC teaching notes
Show the formula, the substitution and the answer with a unit. Correct working earns marks even if you misread a value.General advice from NESA marking feedback, 2021 to 2025, summarised

Summaries in our own words. Read NESA's own feedback with the exam packs: 2024 · 2025.

Where this leads in Year 12

In Year 12 the wave model is applied to light: v = fλ becomes c = fλ for electromagnetic waves, and superposition explains the bright and dark bands of double-slit and diffraction-grating patterns (d sin θ = mλ). The wave model of light is then weighed against the particle model, where each photon has energy E = hf.

FAQ

What is the difference between transverse and longitudinal waves?: In a transverse wave the particles oscillate at right angles to the direction the energy travels (a wave on a rope). In a longitudinal wave they oscillate parallel to it, making compressions and rarefactions (sound). Both carry energy without carrying the medium along.
What is the difference between a displacement–time graph and a displacement–distance graph?: A displacement–distance graph is a snapshot of the whole wave at one instant: crest to crest is the wavelength. A displacement–time graph follows one particle over time: crest to crest is the period. Check the horizontal axis to tell them apart.
Is amplitude measured from crest to trough?: No. Amplitude is the maximum displacement from the rest position, so it is measured from the middle line to a crest. Crest to trough is twice the amplitude.
Does the frequency of a wave change when it enters a new medium?: No. The frequency is set by the source. The speed changes in the new medium, so the wavelength changes too (λ = v/f). This is what happens in refraction.

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