Longitudinal against transverse waves: the difference (vibration along the direction of travel against across it), the labelled diagrams (compression and rarefaction; crest and trough), the examples (sound and P-waves against light, water and S-waves), the slinky demonstration, amplitude, wavelength, frequency and the wave equation v = fλ with worked examples, and a printable sheet with practice

"Longitudinal wave" is searched about 6,800 times a month in the UK and 2,600 in Australia, nearly always by GCSE and Year 9 to 10 students who have been shown a slinky and asked to tell the two kinds of wave apart on paper. The distinction is one sentence long; the marks are in the diagrams, the labels and the wave equation. This page gives the difference, the comparison table, both diagrams with the parts named, the examples that every exam uses, the slinky demonstration, the vacuum and polarisation consequences, the wave equation with four worked examples, and a printable sheet with practice. Our light energy page has the wider classification of waves (mechanical against electromagnetic).

Download the waves sheet with practice (PDF) (A4, the table, the diagrams and the examples on page 1, the wave equation with worked examples and the practice set with answers on page 2, free).

The difference in one sentence

A wave carries energy from one place to another without carrying the material with it; the material only oscillates. The two kinds differ in which way the oscillation points compared with the direction the wave travels:

• Transverse: the oscillation is perpendicular (at right angles) to the direction of travel. Shake one end of a rope up and down; the wave runs along the rope while each bit of rope only moves up and down.
• Longitudinal: the oscillation is parallel to the direction of travel. Push and pull one end of a slinky; the squashed regions run along the slinky while each coil only moves back and forth along it.

The comparison table

The two diagrams, labelled

Transverse. Draw a horizontal line (the rest position) and a sine curve through it. Label: crest (the top of a hump), trough (the bottom of a dip), amplitude (from the rest line to a crest, not crest to trough), wavelength λ (crest to next crest, or any point to the next identical point), and an arrow along the line for the direction of travel with a second, perpendicular arrow for the direction of vibration.

Longitudinal. Draw a row of vertical lines (the particles or coils), bunched close together in some places and spread out in others. Label: compression (lines close together), rarefaction (lines far apart), wavelength λ (middle of one compression to the middle of the next), and two arrows that are both along the row: direction of travel and direction of vibration. The amplitude is how far each particle moves from its rest position, which the diagram cannot show as a height; a question asking you to "mark the amplitude" on a longitudinal diagram is a trap.

A longitudinal wave can also be drawn as a pressure graph (pressure against distance), which looks like a sine curve: compressions are the peaks, rarefactions the troughs. That is not a transverse wave; it is a graph of a longitudinal one.

The slinky demonstration

One slinky shows both. Stretched along a table:

• Flick one end sideways (or up and down): a hump runs along the coils. Each coil moves sideways and back; the hump moves along. Transverse.
• Push the end in and pull it back: a bunched region runs along the coils. Each coil moves along the slinky and back; the compression moves along. Longitudinal.
• Tie a ribbon to one coil. In both cases the ribbon ends up where it started: the wave moved, the material did not.

The same two motions appear in an earthquake. P-waves (primary) are longitudinal, travel fastest (about 6 km/s in the crust) and pass through liquids, so they arrive first and cross the Earth's core. S-waves (secondary) are transverse, slower (about 3.5 km/s) and cannot pass through liquids, which is how we know the outer core is liquid: there is an S-wave shadow on the far side of the Earth.

Why sound cannot cross a vacuum and light can

Sound is a longitudinal wave in a material: it is particles pushing on neighbouring particles. With no particles there is nothing to compress, so sound does not travel through the vacuum of space (the bell-jar experiment: pump the air out and the ringing bell goes silent while still visibly ringing). Light is an electromagnetic wave, an oscillation of electric and magnetic fields rather than of particles, so it crosses empty space at 3.0 × 10⁸ m/s. Sound in air at 20 °C travels at 343 m/s; in water about 1,480 m/s; in steel about 5,000 m/s, faster in stiffer, denser-coupled materials.

Why only transverse waves can be polarised

A transverse wave oscillates in a plane at right angles to its direction; a rope can be shaken up-down or left-right or any angle between. A polarising filter lets through only one of those planes. Light from the sky or reflected off water is partly polarised, which is why polarised sunglasses cut glare and why rotating one filter against another darkens the view. A longitudinal wave oscillates only along its direction of travel; there is no plane to select, so it cannot be polarised. "Sound can be polarised" is a common wrong answer; the fact that it cannot is proof that sound is longitudinal.

Amplitude, wavelength, frequency and the wave equation

• Amplitude (A): the maximum displacement from the rest position, in metres. Bigger amplitude, more energy (louder sound, brighter light).
• Wavelength (λ): the distance between two neighbouring identical points, in metres.
• Frequency (f): how many complete waves pass a point each second, in hertz (Hz). Higher frequency, higher pitch (sound) or bluer colour (light).
• Period (T): the time for one complete wave, in seconds. T = 1 ÷ f.
• Wave speed (v): how fast the energy travels, in m/s.

v = f × λ for every wave, transverse or longitudinal.

Worked examples:

1. A sound wave in air has frequency 500 Hz and wavelength 0.686 m. v = 500 × 0.686 = 343 m/s, the speed of sound at 20 °C.
2. Red light has wavelength 7.0 × 10⁻⁷ m and travels at 3.0 × 10⁸ m/s. f = v ÷ λ = 3.0 × 10⁸ ÷ 7.0 × 10⁻⁷ = 4.3 × 10¹⁴ Hz.
3. Water waves pass a buoy every 4 s, with 6 m between crests. f = 1 ÷ 4 = 0.25 Hz; v = 0.25 × 6 = 1.5 m/s.
4. An ultrasound scanner uses 2 MHz waves, which travel at 1,540 m/s in soft tissue. λ = v ÷ f = 1,540 ÷ 2,000,000 = 7.7 × 10⁻⁴ m, under a millimetre, which is why it resolves small structures.

The mistakes that cost marks

• Defining a transverse wave as one that goes "up and down". It is perpendicular to the direction of travel; a wave along a vertical rope oscillates sideways.
• Marking amplitude from crest to trough (that is twice the amplitude).
• Measuring wavelength from a crest to the next trough (half a wavelength).
• Drawing a longitudinal wave as a sine curve without saying it is a pressure graph.
• Saying sound travels faster in air than in water (it is about four times faster in water).
• Saying sound can be polarised, or that light needs a medium.
• Mixing up frequency (waves per second, Hz) and speed (metres per second).

Where it sits in each curriculum

Practice (answers in the PDF)

1. State the difference between a transverse and a longitudinal wave, and give one example of each.
2. On a longitudinal wave diagram, between which two points would you measure one wavelength?
3. A wave has a frequency of 50 Hz and a wavelength of 4 m. What is its speed?
4. Sound travels at 343 m/s in air. What is the wavelength of a 1,000 Hz note?
5. Why can light from the Sun reach Earth while the sound of its surface cannot?
6. An earthquake's P-waves arrive at a seismometer 40 s before its S-waves. Which type is which, and why do they travel at different speeds?

Download the sheet and the practice set (PDF)

Where to get help

A 1-on-1 online physics class with a tutor who teaches KS3 and GCSE physics, NGSS middle and high-school science, CBSE Class 8 to 11 and the Australian Years 9 to 11 every week: waves taught with a slinky on camera and a diagram drawn together, with the wave equation practised in standard form until it is routine. The physics page lists the courses; the free 30-minute first class is a real lesson on this week's topic. Related pages: light energy and the types of waves and wave phenomena: reflection, refraction, diffraction, interference.

Questions parents ask

See how we teach this, 1-on-1 online →