Parts of a Wave: Crest, Trough, Wavelength, Amplitude
Parts of a wave: a wave has a crest (its highest point), a trough (its lowest point), a wavelength (the length of one complete wave), an amplitude (its height from the rest position), and a frequency (how many waves pass a point each second).
What are the parts of a wave?
A wave is a repeating disturbance that carries energy from one place to another. Each part of a wave has its own name and unit, and the different parts of a wave are set out in the table below. A transverse wave, such as a rope shaken up and down, has these parts:
| Part | Symbol | Unit | What it is |
|---|---|---|---|
| Crest | none | none | The highest point of the wave |
| Trough | none | none | The lowest point of the wave |
| Rest position | none | none | The line the wave would make if nothing were moving |
| Wavelength | λ | m | The distance from one point on a wave to the same point on the next wave, such as crest to crest |
| Amplitude | A | m | The distance from the rest position to the crest (or trough) |
| Frequency | f | Hz | The number of complete waves that pass a point each second |
| Period | T | s | The time for one complete wave, T = 1/f |
What is a crest and a trough?
The crest is the top of a transverse wave and the trough is the bottom. One complete wave goes from a point on the rest position, up to a crest, back through the rest position, down to a trough, and back to the start. Measuring from crest to trough covers only half a wave, so the distance between two crests (or two troughs) is the full wavelength.
What is the difference between wavelength and amplitude?
These two are often confused. Wavelength measures how long one wave is, along the direction the wave travels. Amplitude measures how tall the wave is, from the rest position to the crest. A tall, narrow wave and a short, wide wave can have the same amplitude but different wavelengths.
Amplitude is linked to energy. A louder sound has a larger amplitude, and a brighter light has a larger amplitude. Changing the amplitude does not change the wave speed in the same medium.
How are frequency and period linked?
Frequency and period are two ways of describing how often the wave repeats. They are the reciprocal of each other:
T = 1 ÷ f
A frequency of 2 Hz means two complete waves pass each second, so the period is 0.5 s. A short period means a high frequency, which is a fast-repeating wave.
Longitudinal waves: compressions and rarefactions
Sound is a longitudinal wave, where the particles move back and forth along the direction the wave travels. It has no crests or troughs in the same sense. Instead, it has:
- Compressions, where the particles are pushed closer together. These match the crests.
- Rarefactions, where the particles are spread further apart. These match the troughs.
The wavelength of a sound wave is still the distance from one compression to the next compression.
Worked example: find the wavelength
A wave on a rope has a frequency of 4 Hz and travels at a speed of 12 m/s. What is its wavelength?
- Write the formula: v = fλ, so λ = v ÷ f.
- Substitute: λ = 12 ÷ 4.
- Give the answer with its unit: λ = 3 m.
So each complete wave along the rope is 3 metres long, from one crest to the next. The wave speed formula is explained in full in the wave speed formula article.
Common mistakes
- Measuring wavelength from crest to trough. That distance is half a wavelength. Measure from crest to crest or trough to trough.
- Confusing amplitude with wavelength. Amplitude is the height above the rest position, not the length of one wave.
- Using the period as the frequency. Frequency is waves per second, and period is seconds per wave. They are reciprocals.
- Thinking a higher amplitude makes a wave faster. In the same medium, the speed depends on the medium, not the amplitude.
Frequently asked questions
What are the parts of a wave?
The main parts of a wave are the crest (the highest point), the trough (the lowest point), the rest position (the undisturbed line), the wavelength (the length of one complete wave), the amplitude (the height from the rest position to the crest) and the frequency (the number of waves per second). A wave's period is the time for one complete wave.
What is the difference between wavelength and amplitude?
Wavelength is the distance over which one complete wave repeats, measured in metres. Amplitude is the maximum distance the wave moves from the rest position, also in metres. Wavelength describes the shape of the wave along its length, and amplitude describes how far it rises and falls.
What is a crest and a trough?
A crest is the highest point of a transverse wave, and a trough is the lowest point. The distance between two neighbouring crests, or two neighbouring troughs, is one wavelength. A crest-to-trough distance is only half a wavelength.
How do you measure the wavelength of a wave?
Measure the distance from one point on the wave to the same point on the next wave, such as crest to crest, and read the length in metres. If you can only see part of the wave, you can find the wavelength with v = fλ by dividing the wave speed by the frequency.
Try it yourself
Open the Waves & Sound tool and make waves on the rope. Find the crest, the trough and the rest position in the picture, then measure the wavelength from one crest to the next. Change the frequency and watch the wavelength change while the speed stays the same. For the maths behind it, read the wave speed formula explained.
See it for yourself, in 3D and free.
Try it in the Waves & Sound