What is a wave?

Watch a gull floating on the sea as waves roll past. It bobs up and down and drifts a little, but the waves don't carry it to the shore. NOAA describes ocean waves the same way: the energy moves through the water, while the water itself mostly goes round in small circles. That is the key idea of every wave.

Parts of a wave

Every wave can be described with a few measurements. The graph shows a wave at one instant, like a photo.

Here x is the distance along the wave in metres and y is how far each point is displaced from its rest position, in centimetres. The horizontal line at y = 0 is the rest position, where the material would sit with no wave.

What is the amplitude of a wave?

The amplitude is the maximum displacement of the wave from its rest position. In the graph it is 3 cm: from the rest line up to a crest, or down to a trough. A bigger amplitude means more energy. For sound, a bigger amplitude sounds louder. For light, it means brighter. For a mechanical wave, the energy goes up with the square of the amplitude, so doubling the amplitude carries four times the energy.

What is the frequency of a wave?

The frequency is the number of complete waves passing a point each second, measured in hertz (Hz). 1 Hz means one wave per second. For sound, frequency sets the pitch: a higher frequency is a higher note. Young people can usually hear from about 20 Hz to 20,000 Hz, and the A that orchestras tune to is 440 Hz. Frequency and period are opposites:

Types of waves

Transverse and longitudinal waves

Waves are sorted by which way the material moves compared with the direction the wave travels.

A slinky shows both. Flick one end sideways and a transverse wave runs along it. Push the end in and out and you see bunched-up and stretched-out sections travel along instead: a longitudinal wave. In a longitudinal wave, the wavelength is the distance from one compression to the next.

Mechanical and electromagnetic waves

• Mechanical waves need a material, called a medium, to travel through. Sound, water waves and seismic waves are mechanical. Sound can't cross the vacuum of space, because there is nothing to vibrate.
• Electromagnetic waves are vibrations of electric and magnetic fields, so they need no medium. Light, radio, microwaves and X-rays all travel through empty space at the speed of light, exactly 299,792,458 m/s in a vacuum.

Earthquakes show why the types matter. The USGS explains that P waves are longitudinal and arrive first, while S waves are transverse and slower, and S waves can't travel through liquids. S waves don't pass through Earth's core, which is one way scientists know its outer core is liquid.

The wave equation: v = fλ

In one period T, a wave moves forward by one wavelength λ. Speed is distance ÷ time, so v = λ ÷ T. Since T = 1/f, that becomes:

The speed depends on the medium, not on the source. Sound travels at about 343 m/s in air at 20 °C and much faster in water and steel. So for sound in air, a higher frequency means a shorter wavelength, because their product stays at 343. Our Wave Speed Calculator finds any one of v, f and λ from the other two.

Waves around you

Every wavelength here comes from v = fλ, using 343 m/s for sound and the speed of light for the rest. Microwave ovens run at 2,450 MHz, according to the US Food and Drug Administration. The higher the frequency, the shorter the wavelength, all the way down to light, whose waves are about a two-thousandth of a millimetre long.

Worked examples

Example 1: wave speed

Waves on a pond have a frequency of 5 Hz and a wavelength of 0.6 m. How fast do they travel? v = fλ = 5 × 0.6 = 3 m/s.

Example 2: the wavelength of a note

A tuning fork plays 440 Hz in air, where sound travels at 343 m/s. What is the wavelength? Rearrange to λ = v ÷ f = 343 ÷ 440 = 0.78 m. The lowest note most people can hear, 20 Hz, has a wavelength of about 17 m, and the highest, 20,000 Hz, about 1.7 cm.

Example 3: a radio wave

An FM radio station broadcasts at 100 MHz, which is 100,000,000 Hz. Radio waves travel at the speed of light. What is the wavelength? λ = 299,792,458 ÷ 100,000,000 = 3.0 m to 2 significant figures.

Example 4: period from frequency

A wave has a frequency of 50 Hz. What is its period? T = 1 ÷ f = 1 ÷ 50 = 0.02 s, or 20 milliseconds.

Example 5: how far away is the lightning?

You see a flash and hear thunder 3 seconds later. Light arrives almost instantly, so the delay is the sound's travel time. Distance = speed × time = 343 × 3 = about 1,000 m. That gives the rule of thumb of 3 seconds per kilometre, or about 5 seconds per mile, which is what the National Weather Service uses.

Now try a wave equation question. Answer here, then press Mark to check it in our Light and Energy course.

How to draw a wave

A labelled wave diagram comes up often in tests. To draw a transverse wave neatly:

1. Draw the rest line as a straight horizontal line across the page, in pencil.
2. Mark equal spaces along it. Each pair of spaces will be half a wavelength.
3. Mark the crests and troughs the same distance above and below the line, alternating.
4. Join them with a smooth curve. Keep crests rounded, not pointed, and the same height every time.
5. Label it: an arrow from the rest line to a crest for the amplitude, and an arrow from one crest to the next for the wavelength.

To show a bigger amplitude, draw taller crests with the same spacing. To show a higher frequency at the same speed, squeeze the crests closer together, since the wavelength is shorter. For a longitudinal wave, draw a row of vertical lines bunched together at compressions and spread out at rarefactions.

What waves can do

• Reflection: bouncing off a surface, like an echo or your image in a mirror.
• Refraction: changing direction when the wave changes speed as it enters a new medium, which is why a straw looks bent in water.
• Diffraction: spreading out through a gap or around an obstacle. It is strongest when the gap is about the same size as the wavelength, which is why you can hear round corners.
• Interference: two waves overlapping and adding up. Crest on crest makes a bigger wave, and crest on trough can cancel out. Noise-cancelling headphones use this.

You can see diffraction and interference for yourself in the Wave Interference Simulator.

Common mistakes

• Measuring amplitude from trough to crest. That is twice the amplitude. Measure from the rest line.
• Thinking waves carry matter. They carry energy. The material only moves back and forth around a fixed point.
• Saying a higher frequency travels faster. In one medium all frequencies of sound travel at the same speed. A higher frequency just has a shorter wavelength.
• Forgetting unit prefixes. Convert kHz and MHz to Hz, and cm to m, before using v = fλ.
• Mixing up period and frequency. Period is seconds per wave, and frequency is waves per second.

Read next

Physics · Waves and lightWave speed equation: v = fλ with worked examplesThe wave speed equation v = fλ, the frequency equation f = 1/T, units and rearranging, worked examples for sound, water and light waves, and practice.