The same wave equation
Both are solutions of ∂²u/∂t² = v²·∂²u/∂x². Nothing in that equation cares which way u points — the direction of the displacement is the only thing that separates them.
Home Transverse vs Longitudinal
Head to HeadTransverse vs Longitudinal WavesEvery Difference and Every Similarity, Side by Side
Two wave families, one distinction: whether the medium moves across the direction of travel or along it. Everything else — polarization, which materials each can cross, which seismic wave arrives first — follows from that single fact.
Transverse and longitudinal waves differ in one thing: the direction the medium oscillates relative to the direction the wave travels. Transverse waves oscillate perpendicular to travel and form crests and troughs; longitudinal waves oscillate parallel to travel and form compressions and rarefactions. Only transverse waves can be polarized. Transverse mechanical waves need a solid, while longitudinal waves cross solids, liquids and gases alike — which is why seismic P-waves pass through Earth's liquid outer core and S-waves do not. Light is transverse; sound is longitudinal. Both obey v = f λ, both carry energy without carrying matter, and surface waves such as water ripples are in fact both at once.
Side by Side
The same wave, drawn both ways
Both panels below run on identical values of amplitude, wavelength and frequency, locked to the same phase. Change any control and both respond in exactly the same way. The only thing that differs is the direction each tracked particle is allowed to move.
If you want either family on its own first, there is a full guide to transverse waves and another to longitudinal waves.
This interactive comparison needs a browser with canvas support. The table and the written comparison below cover the same ground.
Shared wave speed2.00m/s — identical for both
Shared period1.00seconds — identical for both
Watch the two coral particles. The upper one is confined to a vertical line; the lower one to a horizontal line. That constraint is the entire difference between the two wave families.
Test Yourself
Is it transverse or longitudinal?
Pick any wave and find out which family it belongs to — and why. Two of these have a more interesting answer than you might expect.
The Full Table
Transverse vs longitudinal: complete comparison
Every property that distinguishes the two, in one place. Highlighted rows are the ones exam questions ask about most.
| Property | Transverse wave | Longitudinal wave |
|---|---|---|
| Particle motion | Perpendicular (90°) to the direction of travel | Parallel to the direction of travel |
| Also called | Shear wave, when mechanical | Compression wave, compressional wave, pressure wave |
| Wave features | Crests and troughs | Compressions and rarefactions |
| What actually varies | Displacement across the path of travel | Density and pressure along the path of travel |
| Can be polarized? | Yes | No |
| Travels through solids? | Yes | Yes |
| Through the interior of liquids and gases? | Mechanical types: no | Yes |
| Through a vacuum? | Electromagnetic types: yes. Mechanical types: no | Never |
| Restoring force | Shear rigidity, or the electromagnetic field itself | Compressibility — the medium springing back |
| Speed in an elastic solid | v = √(G / ρ) | v = √((K + 4G/3) / ρ) |
| Relative speed in the same solid | Slower | Faster — about 1.7× in typical rock |
| Seismic name | S-wave (secondary) | P-wave (primary) |
| Speed in Earth's crust | 3–6 km/s | 6–13 km/s |
| Energy carried | ∝ amplitude² | ∝ amplitude² |
| Governing equation | The same wave equation | The same wave equation |
| Everyday examples | Light, radio waves, a guitar string, water ripples, seismic S-waves | Sound, ultrasound, sonar, a spring pulse, seismic P-waves |
Common Ground
What the two have in common
Comparisons tend to dwell on the differences, which makes the two families look more alien to each other than they are. Almost everything about them is shared.
v = f λ, always
The universal wave equation applies unchanged to both. Frequency times wavelength gives the speed whether the medium is bobbing sideways or bunching along the path.
Energy moves, matter does not
In both cases the particles oscillate about a fixed rest position and return to it. A floating leaf bobs as ripples pass; an air molecule shuffles back and forth as sound passes. Neither travels with the wave.
The same five properties
Amplitude, wavelength, frequency, period and speed describe both completely. Only the way you measure wavelength on a diagram changes: crest to crest, or compression to compression.
Energy scales with amplitude squared
Double the amplitude of either and you carry four times the energy. This is why loudness and brightness both climb so steeply with amplitude.
All the same wave behaviours
Both reflect, refract, diffract, interfere and form standing waves. Echoes and mirages are the same physics applied to sound and to light.
Speed is set by the medium
Neither carries its speed with it. Stiffness and density fix the speed of a mechanical wave of either type, which is why both slow down or speed up when the material changes.
The Mathematics
One equation, two directions
The deepest answer to "what is the difference" is almost disappointing: there isn't one, in the governing equation. Both wave types satisfy the same second-order wave equation.
∂²u/∂t² = v² · ∂²u/∂x²u is the displacement of the medium; v is the wave speed
What changes is the direction of the displacement vector urelative to the direction the wave travels. If u points along the direction of propagation, the wave is longitudinal. If u lies in the plane perpendicular to it, the wave is transverse. In the language of vector calculus, a longitudinal wave is curl-free and a transverse wave is divergence-free, and any general disturbance in an elastic solid splits cleanly into one of each.
Why the longitudinal wave is always faster
That split is exactly what an earthquake performs. The two parts travel at different speeds, and the reason is visible in the formulas:
Longitudinal — P-wavev = √((K + 4G/3) / ρ)
Resists compression and shear: bulk modulus K plus shear modulus G.
Transverse — S-wavev = √(G / ρ)
Resists shear alone: shear modulus G only.
The longitudinal formula contains everything the transverse one has, plus the bulk modulus term. Since K and G are both positive, the longitudinal wave is always faster in the same material. For rock with a typical Poisson's ratio of 0.25, the ratio works out at exactly √3, or about 1.73 — which is why P-waves reliably beat S-waves to every seismograph on Earth.
Now set G = 0, as it is in any liquid or gas, which flows rather than resisting shear. The transverse speed collapses to √(0/ρ) = 0: the wave cannot exist at all. The longitudinal speed becomes √(K/ρ), which is perfectly finite. That single substitution explains the S-wave shadow zone, why sound crosses the ocean, and why a transverse mechanical wave cannot.
The Decisive Test
Polarization tells them apart for good
Of all the differences, one is not a matter of degree. A transverse wave can be polarized and a longitudinal wave cannot — ever, by any means.
A transverse wave oscillates somewhere within the plane perpendicular to its travel. That plane holds infinitely many possible directions: vertical, horizontal, and everything between. A polarizing filter admits one and blocks the rest, which is what sunglasses and LCD screens do to light.
A longitudinal wave has one available direction of oscillation — forward and back along its own path. There is no second direction to remove, so there is nothing a filter could do. No sound polarizer exists, and none can.
This settled a real argument. Through the 1700s many physicists believed light was a longitudinal pressure wave in the aether. Malus's discovery of polarization in 1808, and Young and Fresnel's work in 1817 and 1821, forced the conclusion that light is entirely transverse. Polarization was the evidence that decided it.
The Edge Case
The waves that are both at once
Textbooks present the two families as exhaustive. They are not. Waves travelling along a surface combine both motions, moving each particle around a closed loop rather than along a line.
Follow the coral particle. It rises and falls (transverse) while also moving forward and back (longitudinal) — tracing a circle that closes on itself.
Water waves
A floating object on a passing wave does not simply bob. It moves forward as the crest reaches it, rises, moves backward in the trough and sinks, returning close to where it began. The orbit is near-circular at the surface and shrinks rapidly with depth, becoming negligible below about half a wavelength down. Water waves are usually taught as transverse because the vertical motion is what you see, but the horizontal component is genuinely there.
Rayleigh waves
The seismic equivalent, and the reason earthquakes are so destructive. Rayleigh wavestravel along Earth's surface with particles tracing retrogradeellipses — counter-clockwise for a wave moving right, the opposite sense to a water wave. The major axis of the ellipse is perpendicular to the surface, and the motion dies away with depth. Below roughly a fifth of a wavelength the sense of rotation flips and becomes prograde.
Surface waves arrive after both P and S waves, travel more slowly, and lose energy with distance more gradually — which is why the strongest shaking in a distant earthquake often arrives last.
The Natural Experiment
P-waves vs S-waves: the comparison Earth runs for us
Every earthquake launches a longitudinal wave and a transverse wave from the same point, at the same instant, through the same rock. Nothing differs except the wave type — so the gap between their arrivals measures the difference directly.
A seismogram trace. The longitudinal P-wave arrives first, the transverse S-wave second, and the surface waves last and largest.
That gap is useful. Because the two speeds are known, the delay between the P and S arrivals converts directly into distance from the epicentre — the S–P interval. Readings from three stations triangulate the quake's location, which is how every earthquake you have ever seen reported was located.
The same comparison mapped the planet. S-waves vanish beyond about 103° from an epicentre while P-waves continue to arrive, and the only explanation is a liquid layer that transverse waves cannot cross. Richard Dixon Oldham inferred a core from this in 1906; Inge Lehmann found the solid inner core inside it in 1936. The entire deep structure of Earth was read from the difference between a transverse wave and a longitudinal one.
Get It Right
Six things people get wrong
MythTransverse waves can't travel through liquids at all.
FactMechanical transverse waves can't travel through the *interior* of a liquid, because a fluid has no shear rigidity. They travel across the surface perfectly well — that's what a ripple is — and electromagnetic transverse waves pass straight through water.
MythLongitudinal waves are slower because they're mechanical.
FactIn the same solid, the longitudinal wave is always the faster of the two. Its speed depends on bulk modulus plus shear modulus; the transverse wave gets shear modulus alone. That is precisely why P-waves arrive before S-waves.
MythSound can be polarized with the right filter.
FactIt cannot, at any price. Polarization selects one oscillation direction out of many, and a longitudinal wave only has one to begin with. The impossibility is structural, not technological.
MythThe particles travel along with the wave.
FactNeither type carries matter. Particles oscillate about a rest position and return to it. Only energy and the pattern move forward.
MythEvery wave is either transverse or longitudinal.
FactSurface waves are both at once. Water waves and seismic Rayleigh waves move particles in circles or ellipses, combining the two motions.
MythAmplitude changes how fast a wave travels.
FactIt does not, for either type. Speed is set by the medium. Amplitude sets the energy carried — loudness for sound, brightness for light.
Practice
Head-to-head worked examples
Same numbers, both wave types
A wave has f = 250 Hz and λ = 1.4 m. Find its speed if it is (a) transverse on a string, (b) longitudinal in air.
v = fλ = 250 × 1.4 = 350 m/s in both cases. The equation does not care about the wave type.
P-wave and S-wave from the same quake
In granite the P-wave travels at 5,500 m/s and the S-wave at 3,200 m/s. How far apart are their arrivals after 60 km?
t_P = 60,000/5,500 ≈ 10.9 s, t_S = 60,000/3,200 = 18.75 s. The S-wave arrives about 7.8 s later.
Turning the S–P interval into a distance
A station records the S-wave 24 s after the P-wave, with speeds of 8 and 4.6 km/s. How far away was the epicentre?
d = Δt / (1/v_S − 1/v_P) = 24 / (1/4.6 − 1/8) ≈ 24 / 0.0924 ≈ 260 km.
Why the ratio is about 1.7
For rock with a Poisson's ratio of 0.25, what is v_P / v_S?
v_P/v_S = √(2(1−ν)/(1−2ν)) = √(2 × 0.75 / 0.5) = √3 ≈ 1.73.
The same amplitude change, both ways
Triple the amplitude of a light wave and of a sound wave. What happens to the energy of each?
E ∝ A² for both, so 3² = 9. Each carries nine times the energy.
Why there are no S-waves in the core
A liquid has shear modulus G = 0. What does v_S = √(G/ρ) give?
v_S = √(0/ρ) = 0. A transverse mechanical wave cannot propagate at all — the mathematical reason for the S-wave shadow zone.
Quick Reference
How to tell them apart in ten seconds
- Look at the particle-motion arrow. Across the direction of travel means transverse. Along it means longitudinal.
- Look at the shape. Crests and troughs means transverse. Bunching and spreading means longitudinal.
- Ask whether it can be polarized. Yes means transverse. No means longitudinal.
- Ask whether it crosses a vacuum. Yes means a transverse electromagnetic wave. Never means longitudinal.
- Ask whether it crosses liquid. Through the interior means longitudinal. Blocked means a mechanical transverse wave.
- Check which arrives first. In seismology the faster arrival is always the longitudinal P-wave.
- Watch for circles. If the particles orbit rather than oscillate along a line, it is a surface wave — and it is both.
FAQ
Transverse vs longitudinal waves: common questions
What is the main difference between transverse and longitudinal waves?
The direction the medium moves relative to the direction the wave travels. In a transverse wave the particles oscillate perpendicular — at 90 degrees — to the direction of travel, producing crests and troughs. In a longitudinal wave they oscillate parallel to it, producing compressions and rarefactions. Every other difference, including polarization and which materials each can cross, follows from that one geometric fact. Light is transverse; sound is longitudinal.
What do transverse and longitudinal waves have in common?
A great deal. Both obey the same wave equation and the same relationship v = fλ. Both are described by amplitude, wavelength, frequency, period and speed. Both carry energy without carrying matter, both carry energy proportional to the square of their amplitude, and both reflect, refract, diffract, interfere and form standing waves. For mechanical waves of either type, speed is fixed by the stiffness and density of the medium rather than by the wave itself.
Can a wave be both transverse and longitudinal?
Yes. Surface waves are both at once. In a water wave the particles trace circles, combining up-and-down transverse motion with back-and-forth longitudinal motion. Seismic Rayleigh waves do the same in rock, with particles following retrograde ellipses whose width shrinks with depth. Treating every wave as strictly one or the other is a useful simplification, not a rule of nature.
Why can transverse waves be polarized but longitudinal waves cannot?
Polarization works by allowing one direction of oscillation through and blocking the rest. A transverse wave oscillates somewhere in the plane perpendicular to its travel, so there is a whole plane of directions to choose from. A longitudinal wave oscillates along one axis only — the direction it is travelling — so there is nothing to select and nothing to block. This is the decisive experimental test: light can be polarized, which proves it is transverse; sound cannot, which proves it is longitudinal.
Why do P-waves travel faster than S-waves?
Because they resist different kinds of deformation. A longitudinal P-wave travels at √((K + 4G/3)/ρ), where K is the bulk modulus and G the shear modulus. A transverse S-wave travels at √(G/ρ), using the shear modulus alone. The P-wave formula contains everything the S-wave formula has, plus the bulk modulus term, so the P-wave is always faster in the same material — typically by a factor of about 1.7 in rock.
Why can't transverse mechanical waves travel through liquids and gases?
A transverse mechanical wave works by shearing the medium sideways, which needs the material to resist that shear and spring back. Liquids and gases simply flow instead, so the shear modulus is zero and the wave speed √(G/ρ) becomes zero. Longitudinal waves rely on compression instead, and every material can be compressed, so they pass through all three states. This is exactly why S-waves stop at Earth's liquid outer core while P-waves continue.
Are water waves transverse or longitudinal?
Neither, strictly. A surface water wave is a combination of both. Each water particle travels in a roughly circular orbit as the wave passes, moving forward at the crest and backward in the trough while also rising and falling. Water waves are often taught as transverse because the up-and-down motion is the visible part, but the forward-and-backward component is genuinely there.
Which type of wave is light, and which is sound?
Light is transverse and sound is longitudinal. Light is an electromagnetic wave whose electric and magnetic fields oscillate perpendicular to its direction of travel, which is why it can be polarized and why it crosses the vacuum of space. Sound is a mechanical pressure wave whose molecules oscillate along the direction of travel, which is why it cannot be polarized and cannot cross a vacuum.
Do transverse and longitudinal waves use the same equations?
The general ones, yes. Both satisfy the same wave equation and both obey v = fλ, T = 1/f and E ∝ A². The equations diverge only when you calculate speed from material properties, because each wave type depends on a different elastic modulus: √(G/ρ) for a transverse wave in a solid, √((K + 4G/3)/ρ) for a longitudinal one.
How can you tell from a diagram whether a wave is transverse or longitudinal?
Look at what the arrows do. If the wave is drawn as a smooth sine curve with labelled crests and troughs, and the particle-motion arrow points across the direction of travel, it is transverse. If it is drawn as a row of lines or dots that bunch together and spread apart, with the particle-motion arrow pointing along the direction of travel, it is longitudinal. The wavelength is measured crest to crest in the first case and compression to compression in the second.
Keep Going
Explore further
What Is a Transverse Wave?
The full guide to transverse waves: definition, diagram, properties and examples.
What Is a Longitudinal Wave?
Compressions, rarefactions, the speed of sound and the Doppler effect.
Interactive Simulator
Drag amplitude, frequency and wavelength and watch a wave respond.
Wave Calculator
Solve v = fλ, period, string speed and energy ratios.
Seismic S-Waves
How the S-wave shadow zone revealed Earth's liquid core.
Glossary
Every wave term on this site, defined and cross-linked.