A longitudinal wave has no crests or troughs to point at, so how do we measure its wavelength, frequency and amplitude? The answer is to look at the pattern of squeezed-together and spread-apart particles. Once you can see compressions and rarefactions as the longitudinal equivalent of crests and troughs, every measurement you learned for transverse waves carries straight across to sound.
You push and pull the end of a slinky along its length, sending a longitudinal wave down it.
Before reading: a longitudinal wave has no crest or trough. So what plays the role of a "crest", where would you measure one wavelength? Write your prediction.
The crowded and sparse regions that make up a longitudinal wave
A longitudinal wave is a travelling pattern of squeezed-together particles (compressions) chasing spread-apart particles (rarefactions), and these regions are the longitudinal stand-ins for crests and troughs.
As a longitudinal wave passes, particles bunch up in some places and spread out in others. A compression is a region where particles are crowded together, high density and high pressure. A rarefaction is a region where particles are spread apart, low density and low pressure. These regions move along with the wave; a compression is the longitudinal equivalent of a crest, and a rarefaction the equivalent of a trough.
A compression is a region of crowded, high-pressure particles; a rarefaction is a region of spread-out, low-pressure particles. Compressions and rarefactions are the longitudinal equivalents of crests and troughs.
Pause, copy the highlighted statement into your book before moving on.
Did you get this? True or false: in a longitudinal sound wave, a rarefaction is a region where the air particles are spread further apart than normal.
Measuring a longitudinal wave between its compressions
We just identified compressions and rarefactions. That raises a question: if there are no crests, where do we measure one wavelength? This card answers it → from one compression to the very next compression.
Because a compression is the "crest" of a longitudinal wave, one wavelength is simply the distance from one compression to the next, and frequency and period mean exactly what they did for transverse waves.
The wavelength $\lambda$ of a longitudinal wave is the distance between two successive compressions (or two successive rarefactions). The frequency $f$ is how many compressions pass a fixed point each second (in Hz), and the period $T$ is the time for one full cycle to pass, still linked by $T = 1/f$.
$\lambda$ = distance between successive compressions $\qquad T = \dfrac{1}{f}$
In a sound wave travelling along a tube, successive compressions are $0.40\ \text{m}$ apart, and $170$ compressions pass a point each second. Find the wavelength and the period.
For a longitudinal wave, wavelength is the distance between successive compressions; frequency is the number of compressions passing per second; period is the time for one cycle, with $T = 1/f$.
Add the highlighted definitions to your notes before the check below.
Quick check: In a longitudinal wave, which distance equals one wavelength?
Pattern A, Match then explain
In your book draw a longitudinal wave as a row of dots showing two compressions and two rarefactions. (1) Label one wavelength. (2) Build a "translation table" matching each transverse term to its longitudinal partner: crest ↔ ?, trough ↔ ?, and explain how amplitude is shown in each case. (3) State what increasing the amplitude does to the energy carried.
Two truths, one lie: Two truths and a lie about describing a longitudinal wave. Which statement is the lie?
Dot point: Describe the wavelength, frequency, period, compression, rarefaction and amplitude of longitudinal waves
How "big" a longitudinal wave is, and why it matters for sound
We just measured a longitudinal wave's spacing and timing. That raises a question: what does amplitude mean when there is no visible "height"? This card answers it → the maximum distance each particle is pushed from its rest position.
The amplitude of a longitudinal wave is how far each particle swings back and forth from its rest spot along the line of travel, and the bigger that swing, the more crowded the compressions, the higher the pressure, and the more energy the wave carries.
In a longitudinal wave each particle oscillates back and forth along the direction of travel. The amplitude is the maximum displacement of a particle from its rest position. A larger amplitude means particles are pushed further, so compressions are denser (higher pressure) and rarefactions sparser, and the wave carries more energy. For sound this is what we hear as loudness: bigger amplitude, louder sound.
Amplitude of a longitudinal wave is the maximum displacement of a particle from its rest position along the line of travel. Greater amplitude means denser compressions, higher pressure variation and more energy (louder sound).
Pause, copy the highlighted statement into your book before the check below.
Last check: Decide if the statement is true or false.
Increasing the amplitude of a longitudinal wave increases the energy it carries.
Fill the gaps: Complete the description of a longitudinal wave, then press Check.
A region of high particle density is a and a region of low particle density is a . One wavelength is measured between two adjacent . The maximum displacement of a particle from its rest position is the .
Dot point: Describe the wavelength, frequency, period, compression, rarefaction and amplitude of longitudinal waves
A fresh set drawn from this lesson's question bank, feedback shown immediately. +5 XP per correct · +25 XP all correct
Pick your answer, then rate your confidence, that tells the system what to drill next.
UnderstandBand 4(4 marks) 1. Describe what is meant by compression, rarefaction, wavelength and amplitude for a longitudinal sound wave.
1 mark: compression, particles crowded / high pressure · 1 mark: rarefaction, particles spread / low pressure · 1 mark: wavelength, distance between successive compressions · 1 mark: amplitude, maximum displacement of a particle from rest (relates to energy/loudness)
ApplyBand 4(3 marks) 2. A loudspeaker produces a sound wave in air. Successive compressions are $0.68\ \text{m}$ apart, and the cone completes $500$ oscillations each second. State the wavelength and the frequency of the wave, and describe what a single air particle does as the wave passes.
1 mark: wavelength $= 0.68\ \text{m}$ (compression to compression) · 1 mark: frequency $= 500\ \text{Hz}$ · 1 mark: the particle oscillates parallel to the direction of travel about a fixed rest position
Dot point: Describe the wavelength, frequency, period, compression, rarefaction and amplitude of longitudinal waves
AnalyseBand 5(3 marks) 3. Explain how the terms crest and trough, used for a transverse wave, correspond to features of a longitudinal wave, and identify one way in which the correspondence can mislead a student.
1 mark: compression corresponds to a crest · 1 mark: rarefaction corresponds to a trough · 1 mark: identifies that the longitudinal features are density or pressure variations along the direction of travel, not sideways displacements
Dot point: Describe the wavelength, frequency, period, compression, rarefaction and amplitude of longitudinal waves
MC answers and full explanations are shown inline as you complete each question. Use the retry button to attempt a fresh set from the lesson bank.
Q1 (4 marks): A compression is a region of the wave where particles are crowded together, giving high density and high pressure. A rarefaction is a region where particles are spread apart, giving low density and low pressure. The wavelength is the distance between two successive compressions (or two successive rarefactions). The amplitude is the maximum displacement of a particle from its rest position along the direction of travel; a larger amplitude means the wave carries more energy, heard as a louder sound.
Q2 (3 marks): One wavelength of a longitudinal wave is the distance covering one complete cycle of the pressure pattern, measured between two adjacent compressions, so $\lambda = 0.68\ \text{m}$. The frequency is the number of complete oscillations produced each second, so $f = 500\ \text{Hz}$. A single air particle does not travel with the sound: it oscillates back and forth parallel to the direction the wave travels, about a fixed rest position, moving closer to its neighbours as a compression passes and further from them as a rarefaction passes.
Q3 (3 marks): When a longitudinal wave is plotted as pressure or particle density against position, a compression appears where the graph peaks and so corresponds to a crest, while a rarefaction appears where the graph is lowest and so corresponds to a trough. The correspondence can mislead because it is only a correspondence on a graph. In a transverse wave the crest is a real sideways displacement of the medium; in a longitudinal wave nothing moves sideways at all. The particles oscillate back and forth along the direction of travel, and the compression is a region of crowding, not a bump. A student who pictures a longitudinal wave as literally wave-shaped will misdescribe the particle motion.
You can now describe a longitudinal wave with the same precision as a transverse one, compression and rarefaction in place of crest and trough, wavelength between compressions, and amplitude as particle displacement. Next lesson links all of these together in the wave equation $v = f\lambda$.
↩ Back to focus-area hubAt the start you predicted where a wavelength sits in a wave with no crests. The answer is between one compression and the next, the compression is the longitudinal "crest". With that single translation, every measurement you learned for transverse waves carries straight across to sound.
A short spaced-retrieval set, mixing this lesson with earlier ones. It gets harder to guess and easier to remember.
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