Transverse and longitudinal waves

What is a transverse wave?

Tie one end of a rope to a post and flick the other end up and down. A wave runs along the rope towards the post, but each bit of rope only moves up and down. The movement (the oscillation) is perpendicular, at 90°, to the direction the wave and its energy travel. That makes it a transverse wave.

Here x is the distance along the rope in metres and y is how far each point is displaced up or down, in centimetres. A transverse wave has:

• Crests (peaks) and troughs: the highest and lowest points.
• Amplitude: the largest displacement from the rest position, here 2 cm. It is measured from the middle to a crest, not from crest to trough.
• Wavelength (λ): the length of one complete wave, crest to crest, here 4 m.
• Frequency (f): how many waves pass a point each second, in hertz (Hz).

Try it: this question asks you to label the parts of a wave.

Examples of transverse waves

• Ripples on water. AQA uses these as its example of a transverse wave.
• All electromagnetic waves: light, radio waves, microwaves, X-rays and the rest. Here it is electric and magnetic fields that oscillate, not particles.
• Waves on a string, such as a guitar or violin string.
• Seismic S-waves from earthquakes, which shake the ground from side to side.

What is a longitudinal wave?

Now lay a slinky spring on a table and push one end in and out. Bunched up sections travel along it, with stretched out sections in between. Each coil moves backwards and forwards along the same line the wave travels. The oscillation is parallel to the direction of travel, which makes it a longitudinal wave.

• Compression: where the particles are squeezed close together, so the pressure is higher.
• Rarefaction: where the particles are spread out, so the pressure is lower.
• Wavelength: the distance from one compression to the next. In the diagram, the compressions are 3.6 units apart.

Examples of longitudinal waves

• Sound waves in air and water. AQA states that sound waves travelling through air are longitudinal. Our guide to sound waves covers them in detail.
• Ultrasound, used in medical scans and sonar.
• Seismic P-waves, the first waves to arrive after an earthquake.
• A slinky pushed and pulled along its length.

Transverse vs longitudinal waves

Polarisation is an A-level idea that tells the two apart. A polarising filter only lets through vibrations in one plane. Transverse waves, which can vibrate in many planes at right angles to their travel, can be filtered this way; longitudinal waves, which only vibrate along their direction of travel, can't. Polarised sunglasses work because light is transverse.

What is a mechanical wave?

A mechanical wave is a wave that travels through a material, called the medium, by making its particles vibrate and pass the vibration on. Sound, water waves, waves on strings and seismic waves are all mechanical. Mechanical waves can be transverse or longitudinal, but they can't cross a vacuum, because there are no particles to carry them.

The other big family is electromagnetic waves, which are vibrating electric and magnetic fields. They need no medium, so light from the Sun reaches us across empty space. All electromagnetic waves are transverse. In solids, mechanical waves can travel both ways at once, as OpenStax University Physics notes, which is why earthquakes produce both P-waves and S-waves.

Waves carry energy, not matter

In both kinds of wave, the particles only vibrate about a fixed spot; they don't travel with the wave. A duck on a pond bobs up and down as ripples pass under it rather than being carried to the bank. What travels is the energy, and the information the wave carries.

The wave equation

Transverse and longitudinal waves both follow the same equation, from the AQA GCSE specification: wave speed = frequency × wavelength.

• Transverse example: ripples in a tank have a frequency of 4 Hz and a wavelength of 0.15 m. Their speed is 4 × 0.15 = 0.6 m/s.
• Longitudinal example: compressions on a slinky are 0.4 m apart and 5 pass each second. The wave travels at 5 × 0.4 = 2 m/s.

Check these in our Wave Speed Calculator, then try a question on the wave equation:

Common mistakes

• Measuring amplitude from crest to trough. That is twice the amplitude.
• Saying sound is transverse. In air it is longitudinal; the wavy line on an oscilloscope is a graph of pressure.
• Saying the particles travel with the wave. They vibrate in place; energy travels.
• Saying "at right angles to the wave". Be precise: perpendicular to the direction the energy moves.
• Thinking all transverse waves can cross a vacuum. Only electromagnetic ones can. Ripples and waves on strings are transverse but mechanical.
• Mixing up P and S. P for push and pull (longitudinal); S for shake side to side (transverse).

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