"Big waves", "fast waves", "long waves", everyday language is too vague to do physics with. To calculate, predict and compare waves, we need exact measurements: how tall, how far apart, how often. This lesson gives you the six precise terms that turn a wiggly line into a wave you can put numbers on, wavelength, frequency, period, crest, trough and amplitude.
A wave on a string repeats the same shape over and over as it travels.
Before reading: if you had to measure "how big" and "how often" a wave is using only a ruler and a stopwatch, what two quantities would you measure, and what would you measure them between? Write your idea.
How "tall" a wave is, measured from rest, not peak to peak
A transverse wave has high points called crests and low points called troughs; how far a particle swings from its undisturbed rest position is the amplitude, and it sets how much energy the wave carries.
Draw the wave's rest position as a horizontal line. A point of the wave that rises above it to a maximum is a crest; a point that dips below to a minimum is a trough. The amplitude $A$ is the distance from the rest line up to a crest (equal to the distance down to a trough). A common trap is to measure crest-to-trough, that is twice the amplitude. Larger amplitude means the wave carries more energy.
A crest is the highest point and a trough the lowest point of a transverse wave. Amplitude ($A$) is the maximum displacement from the rest position to a crest (or trough); greater amplitude means more energy.
Pause, copy the highlighted statement into your book before moving on.
Did you get this? A wave has crests $0.8\ \text{m}$ above the rest line and troughs $0.8\ \text{m}$ below it. What is its amplitude?
The length of one complete wave
We just saw how to measure a wave's height. That raises a question: how do we measure its length along the direction of travel? This card answers it → with the wavelength, the distance over which the wave repeats.
Wavelength is simply how far you travel along the wave before the pattern repeats, most easily measured from one crest to the very next crest.
The wavelength $\lambda$ (Greek "lambda") is the distance between two successive points that are in the same stage of their motion, crest to next crest, trough to next trough, or any point to the matching point one cycle later. It is measured in metres. A short wavelength means the wave repeats quickly in space (choppy); a long wavelength means it repeats slowly (rolling).
$\lambda$ = distance between successive matching points (crest → next crest), measured in metres (m)
On a string, successive crests are found at the $1.2\ \text{m}$, $1.95\ \text{m}$ and $2.70\ \text{m}$ marks. What is the wavelength of the wave?
Wavelength ($\lambda$) is the distance between two successive matching points on a wave (crest to next crest, or trough to next trough), measured in metres.
Add the highlighted definition to your notes before the check below.
Quick check: True or false: the distance from a crest to the next trough is one wavelength.
Pattern A, Sketch then calculate
In your book sketch one and a half wavelengths of a transverse wave with a rest line. Label a crest, a trough, the amplitude and one wavelength. Then answer: a wave has an amplitude of $3\ \text{cm}$ and a period of $0.25\ \text{s}$. (1) How far apart, vertically, are a crest and a trough? (2) What is the wave's frequency?
Fill the gaps: Fill each blank with the correct term for a transverse wave, then press Check.
The highest point of a transverse wave is a , and the lowest point is a . The maximum displacement from the rest position is the , and the distance from one crest to the next is the .
Dot point: Describe the wavelength, frequency, period, crest, trough and amplitude of transverse waves
Two ways of saying the same thing about timing
We just measured a wave in space (wavelength). That raises a question: how do we measure it in time, how often does a full wave pass? This card answers it → with frequency and period, which are reciprocals.
Frequency counts how many complete waves pass a point each second, while period is the time for just one wave, and because they describe the same timing, one is simply the flip of the other.
The frequency $f$ is the number of complete waves (cycles) passing a fixed point each second, measured in hertz (Hz). The period $T$ is the time taken for one complete wave to pass, in seconds. They are reciprocals:
$$T = \frac{1}{f} \qquad\qquad f = \frac{1}{T}$$
So a wave with frequency $5\ \text{Hz}$ has a period of $\tfrac{1}{5} = 0.2\ \text{s}$. High frequency ⇒ short period; low frequency ⇒ long period.
Frequency ($f$) is the number of complete waves per second (Hz); period ($T$) is the time for one complete wave (s). They are reciprocals: $T = 1/f$.
Pause, copy the highlighted relationship into your book before the check below.
Last check: A wave has a period of $0.02\ \text{s}$. What is its frequency?
Match them up: Match each property of a transverse wave to the quantity it describes.
Dot point: Describe the wavelength, frequency, period, crest, trough and amplitude of transverse 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. A transverse wave has a wavelength of $0.60\ \text{m}$ and a frequency of $4.0\ \text{Hz}$. Define wavelength and frequency, and calculate the period of this wave.
1 mark: wavelength defined (distance between successive matching points) · 1 mark: frequency defined (complete waves per second) · 1 mark: correct formula $T = 1/f$ · 1 mark: $T = 0.25\ \text{s}$
ApplyBand 4(3 marks) 2. A transverse water wave has crests $2.4\ \text{m}$ apart, and a floating buoy rises and falls through a total vertical range of $0.60\ \text{m}$. The buoy completes $15$ full oscillations in $30\ \text{s}$. State the wavelength, the amplitude and the frequency of the wave, showing how you obtained each.
1 mark: wavelength $= 2.4\ \text{m}$ (crest to crest) · 1 mark: amplitude $= 0.30\ \text{m}$ (half the total range) · 1 mark: frequency $= 0.50\ \text{Hz}$ (15 ÷ 30)
Dot point: Describe the wavelength, frequency, period, crest, trough and amplitude of transverse waves
AnalyseBand 5(3 marks) 3. A student measures the amplitude of a transverse wave by reading the vertical distance from a crest down to the next trough. Explain the error this introduces, state the size of the error as a factor, and describe the correct measurement.
1 mark: identifies that crest-to-trough is not the amplitude · 1 mark: states the value obtained is twice the true amplitude · 1 mark: describes measuring from the rest (equilibrium) line to a crest
Dot point: Describe the wavelength, frequency, period, crest, trough and amplitude of transverse 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): Wavelength ($\lambda$) is the distance between two successive matching points on a wave, such as crest to next crest. Frequency ($f$) is the number of complete waves passing a fixed point each second, measured in hertz. The period is the reciprocal of the frequency: $T = 1/f = 1/4.0 = 0.25\ \text{s}$. (The wavelength of $0.60\ \text{m}$ is not needed for the period, it would be used with $v = f\lambda$ to find the speed.)
Q2 (3 marks): The wavelength is the distance of one complete cycle, measured crest to crest, so $\lambda = 2.4\ \text{m}$. The amplitude is the maximum displacement from the rest position, not the full crest-to-trough range, so it is half of $0.60\ \text{m}$, giving $A = 0.30\ \text{m}$. The frequency is the number of complete oscillations per second, so $f = 15 \div 30 = 0.50\ \text{Hz}$. (The period would be $T = 1/f = 2.0\ \text{s}$.)
Q3 (3 marks): Amplitude is defined as the maximum displacement of a particle from its rest position, so it is measured from the undisturbed equilibrium line to a crest (or to a trough). Reading from a crest down to the next trough spans the displacement above the rest line and the displacement below it, so it covers two amplitudes. The student's value would therefore be twice the true amplitude. The correct measurement is to locate the rest line of the wave, which lies midway between crest and trough, and measure the vertical distance from that line to a single crest.
You can now label and measure a transverse wave precisely: crest, trough, amplitude, wavelength, frequency and period. Next lesson applies the matching vocabulary, compression, rarefaction and amplitude, to longitudinal waves.
↩ Back to focus-area hubAt the start you described how to measure "how big" and "how often" a wave is. Now you can name those measurements exactly: amplitude (from the rest line), wavelength (between matching points), and frequency or period (for timing). Two waves with the same speed can differ in wavelength and frequency, but if one has a longer wavelength it must have a lower frequency.
A short spaced-retrieval set, mixing this lesson with earlier ones. It gets harder to guess and easier to remember.
Tell us what you would like help with. Register interest; support details will be confirmed before enrolment.
Register interest →