Transverse vs Longitudinal Waves: The Difference

In a transverse wave the medium is disturbed perpendicular to the direction the wave travels. In a longitudinal wave the disturbance is parallel to it. Sound is longitudinal and light is transverse, and the difference that gets tested is that only a transverse wave can be polarized.

AP Physics: Unit 14 (topics 14.1 Properties of Wave Pulses and Waves, 14.3 Boundary Behavior of Waves and Polarization). The definitions are AP Physics 2 essential knowledge 14.1.A.4 (in a transverse wave the direction of the disturbance is perpendicular to the direction of propagation of the wave) and 14.1.A.5 (in a longitudinal wave the direction of the disturbance is parallel to the direction of propagation of the wave), with 14.1.A.5.i placing sound as a mechanical longitudinal wave and 14.1.A.5.ii naming compressions and rarefactions. The consequence is filed under Topic 14.3: 14.3.A.2.i says transverse waves can be polarized and oscillate in a single plane, and 14.3.A.2.ii says longitudinal waves cannot be polarized. Topic 14.4 places electromagnetic waves as transverse. Neither 14.1 nor 14.3 prints a boundary statement; Unit 14's only three sit under Topics 14.4, 14.5 and 14.9. Unit 14 carries 12 to 15 percent of the multiple-choice section across a suggested 14 to 23 class periods.

The distinction, stated once

Both definitions compare the same two directions, so there is exactly one question to ask: which way does a bit of the medium move, compared with which way the wave goes?

The AP Physics 2 CED puts it in two sentences that are deliberately parallel. Essential knowledge 14.1.A.4: in a transverse wave, the direction of the disturbance is perpendicular to the direction of propagation of the wave. Essential knowledge 14.1.A.5: in a longitudinal wave, the direction of the disturbance is parallel to the direction of propagation of the wave.

Perpendicular means transverse. Parallel means longitudinal. Nothing else in the definition, and in particular nothing about what the wave looks like when it is drawn.

Two placements follow from the CED itself. Sound waves are modeled as mechanical longitudinal waves, which is 14.1.A.5.i. Electromagnetic waves are transverse, because the electric and magnetic field oscillations are perpendicular to the direction of propagation, which Topic 14.4 states.

The reason this is not just vocabulary is that "perpendicular" leaves a choice and "parallel" does not. A wave travelling along a line can be disturbed vertically, horizontally, or at any angle in the plane at right angles to its travel. A wave disturbed along its own line of travel has one option. Everything on the rest of this page comes back to that asymmetry.

Transverse against longitudinal, row by row

Property	Transverse wave	Longitudinal wave
Direction of the disturbance	perpendicular to propagation (14.1.A.4)	parallel to propagation (14.1.A.5)
Named example in the CED	electromagnetic waves, waves on a string	sound waves (14.1.A.5.i)
The two extremes are called	crests and troughs	compressions and rarefactions (14.1.A.5.ii)
How amplitude is read	maximum displacement from equilibrium (14.1.A.6)	maximum increase or decrease in pressure from equilibrium pressure (14.1.A.6.i)
Can it be polarized	yes, it can oscillate in a single plane (14.3.A.2.i)	no (14.3.A.2.ii)
What a picture of it shows	the actual shape of the medium	a graph of pressure or displacement, not a shape
Does it need a medium	mechanical ones do, electromagnetic ones do not (14.1.A.2)	yes, a mechanical longitudinal wave needs a medium
Speed set by	the type of wave and the properties of the medium (14.1.A.3)	the type of wave and the properties of the medium (14.1.A.3)

Read the last row and the one above it together. Wave speed depends on the type of wave and the medium, so a single medium can carry both types at different speeds. A slinky does exactly that, and the worked examples below use it.

Read the compressions and rarefactions row carefully too. The CED's sentence is "the regions of high and low pressure in a sound wave are called compressions and rarefactions, respectively", so high pressure is a compression and low pressure is a rarefaction. The word order in that sentence is the whole rule.

The case that separates them: a polarizing filter

Set up a light beam and a loudspeaker side by side, and put a polarizing filter across each. The light dims. The sound does not change at all. Add a second filter turned ninety degrees to the first and, for ideal filters, the light stops completely while the sound is still exactly as loud as it was.

That is the difference made visible, and the CED grounds every step of it.

14.3.A.2.i says transverse waves can be polarized and oscillate in a single plane. Before the first filter, the light's field oscillations are perpendicular to its travel but spread over every angle in that perpendicular plane. The filter throws away all but one of those angles, so what emerges oscillates in one plane. 14.3.A.3 adds that polarization of a wave may result in a reduction of the wave's intensity, which is the dimming. Turn a second filter to pass only the perpendicular plane and there is nothing left for it to pass.

14.3.A.2.ii says longitudinal waves cannot be polarized. Sound's disturbance is already along one line, the line the sound is travelling on. There is no set of angles to select from, so there is nothing a filter could do. Not "the filter is bad at it": there is no property to filter.

So "can this wave be polarized?" and "is this wave transverse?" are the same question asked twice. That makes the split from 14.1 into something with a consequence, which is why the CED files polarization in Topic 14.3 rather than alongside the definitions.

Note one word in 14.3.A.2. It says transverse waves that are reflected from a surface, refracted through a medium, or pass through specific openings may be polarized. Those processes can polarize a transverse wave, not that they always fully do. Reflected light is not automatically fully polarized, and a question that says "the reflected light is polarized" is telling you something, not restating a rule.

The picture problem, and why it fools people

Draw a transverse wave on a string and the drawing is a photograph. The string really is that shape, and a crest really is a piece of string displaced upwards.

Draw a longitudinal wave and you cannot photograph it the same way, because the interesting motion is along the page rather than across it. So every textbook plots something instead: pressure against position, or displacement against position. Both plots come out as sine curves, and both look exactly like the transverse drawing on the facing page.

They are not the same kind of object.

On the transverse drawing, the vertical axis is a real vertical displacement of real material, and the curve is a shape.
On the longitudinal plot, the vertical axis is a pressure, or a displacement measured along the horizontal axis. The curve is a graph, and the medium is not bent into that shape at all.

Two consequences worth carrying into a question. A peak on a longitudinal pressure plot is a compression, a region where the air is crowded together, not a place where anything moved upwards. And a point of maximum pressure is a point where the air is momentarily not moving, while a point at equilibrium pressure is where the air is moving fastest, which is the opposite of the pairing your eye expects from the transverse picture.

The safe habit is to read the axis labels before reading the curve. Every wave graph in AP Physics 2 is one of the two forms in 14.2.A.2, displacement against time or displacement against position, and the axis tells you which quantity is oscillating. Neither form tells you whether the wave is transverse or longitudinal, and neither is meant to.

When it costs a mark

Calling sound transverse because the graph looks like a sine curve. 14.1.A.5.i is explicit: sound waves are modeled as mechanical longitudinal waves. The graph is a plot, not a picture.
Swapping compressions and rarefactions. High pressure is a compression, low pressure is a rarefaction, in that order in 14.1.A.5.ii.
Saying sound can be polarized with a good enough filter. 14.3.A.2.ii rules it out for every longitudinal wave, and the reason is geometric, not technological.
Saying only light can be polarized. Any transverse wave can be, including a wave on a rope sent through a slotted board. The CED's condition is transverse, not electromagnetic.
Treating "transverse" as a synonym for "electromagnetic". A wave on a string is transverse and mechanical, so it needs a medium. 14.1.A.2 is a separate classification and it does not line up with this one.
Using the split to argue about speed. 14.1.A.3 says speed depends on the type of wave and the properties of the medium. The type matters, but so does the medium, so "longitudinal waves are faster" is not a rule you can quote. In a given material you have to be told, or given the properties.
Assuming the transverse and longitudinal distinction changes the wave equations. It does not. Both obey $\lambda = v/f$ , both reflect and transmit at a boundary, both interfere, both form standing waves, and both keep their frequency when the medium changes.

That last one is the most useful thing to know before an exam. Only the polarization row of the table above actually behaves differently. Everything else is shared, which is exactly why the distinction slips past unnoticed.

When they coincide, and why that lulls you

Almost everything Unit 14 does works identically for both types, and that is the trap.

Both carry energy without carrying matter, which is 14.1.A.1. Both have a speed fixed by the medium, 14.1.A.3. Both have an amplitude, a period, a frequency and a wavelength, and both obey the printed relationship $\lambda = v/f$ from 14.2.A.3. Both split into a reflected and a transmitted part at a boundary, and for both the frequency survives the crossing while the speed and wavelength change, which is 14.3.A.1.iv. Both superpose by adding displacements, 14.6.A.3, so both produce interference, beats and standing waves. A pipe full of air and a string under tension both have a harmonic series, and the algebra behind those two series is the same algebra.

So a student can go a long way computing wavelengths and harmonics without ever needing to know which type of wave is in front of them. The distinction only produces a different answer in one place, and that place is polarization.

There is a second, quieter coincidence: a standing wave in a pipe and a standing wave on a string are drawn the same way. The loops on a diagram of a pipe are not the shape of anything; they represent the displacement amplitude of air moving back and forth along the pipe. Reading them as a shape leads to the wrong end conditions, because a closed pipe end has to be a displacement node, and it looks in the drawing like the exact opposite of an open one. Topic 14.6 works through the four end cases.

Sorting the waves AP Physics 2 names

Wave	Type	Needs a medium	Can be polarized
Light and every other electromagnetic wave	transverse	no	yes
Sound in air, water or a solid	longitudinal	yes	no
A pulse or wave on a string under tension	transverse	yes	yes
A compression pulse sent along a spring	longitudinal	yes	no
Ripples driven across a slinky at right angles	transverse	yes	yes

The table has only two columns that do any work, and they do not agree with each other. Type decides polarization. Whether the wave is mechanical or electromagnetic decides whether it needs a medium. Those are the two independent classifications in 14.1, essential knowledge 14.1.A.2 for the medium and 14.1.A.4 and 14.1.A.5 for the direction, and a question can test either one without touching the other.

The row that catches people is the last two: the same slinky appears as both a transverse and a longitudinal medium, depending only on how you shake it. Nothing about the spring changed. That is the cleanest demonstration that the classification describes the wave, not the material.

One slinky, two wave types, two wavelengths

A long slinky is stretched across a bench. Shaken side to side it carries transverse waves at $3.0\ \text{m/s}$ ; pushed and pulled along its length it carries longitudinal waves at $5.0\ \text{m/s}$ . Both are driven at $2.0\ \text{Hz}$ . (a) Find the wavelength of each. (b) Explain how one medium can have two wave speeds. (c) The transverse driver is turned up so the sideways swing is twice as wide. What happens to the wavelength?

(a) The printed relationship is $\lambda = \dfrac{v}{f}$ , and it applies to both types without modification. For the transverse wave, $\lambda = \dfrac{3.0\ \text{m/s}}{2.0\ \text{Hz}} = 1.5\ \text{m}$ .
For the longitudinal wave, $\lambda = \dfrac{5.0\ \text{m/s}}{2.0\ \text{Hz}} = 2.5\ \text{m}$ .
Check the units: metres per second divided by inverse seconds gives metres. Both answers are lengths, as they must be.
(b) Read 14.1.A.3 exactly: the speed at which a wave propagates through a medium depends on the type of wave and the properties of the medium. Type is in that list. A slinky resists being bent sideways and resists being stretched along its length by different amounts, so the two disturbances travel at different speeds through the same coils.
That is also why 'longitudinal waves are faster' is not a rule to quote. Here the longitudinal wave happens to be faster, but the numbers came from the apparatus, not from the classification.
(c) Nothing. Amplitude is not on 14.1.A.3's list of what sets the speed, so $v$ is unchanged at $3.0\ \text{m/s}$ . The driver still repeats $2.0$ times a second, so $f$ is unchanged too. With both inputs fixed, $\lambda = v/f = 1.5\ \text{m}$ as before. A bigger swing carries more energy, by 14.1.A.6.iii, and that is the only thing that changed.

(a) $1.5\ \text{m}$ transverse and $2.5\ \text{m}$ longitudinal. (b) 14.1.A.3 lists the type of wave alongside the properties of the medium, so one medium can support two speeds. (c) The wavelength stays at $1.5\ \text{m}$ ; only the energy carried goes up.

Compressions, rarefactions and the graph that is not a picture

A loudspeaker emits a pure tone of $686\ \text{Hz}$ into air where the speed of sound is $343\ \text{m/s}$ . (a) Find the wavelength. (b) Find the distance from one compression to the next, and from a compression to the nearest rarefaction. (c) A student plots air pressure against position along the beam and gets a sine curve, then says the air molecules are moving up and down along that curve. Correct them.

(a) $\lambda = \dfrac{v}{f} = \dfrac{343\ \text{m/s}}{686\ \text{Hz}} = 0.500\ \text{m}$ .
(b) 14.2.A.1.vi defines the wavelength as the distance between successive corresponding positions on a wave. Two adjacent compressions are successive corresponding positions, so they are one full wavelength apart: $0.500\ \text{m}$ .
A compression is a maximum of pressure and a rarefaction is a minimum, so the nearest rarefaction is half a cycle away: $\dfrac{0.500}{2} = 0.250\ \text{m}$ .
Check with 14.1.A.5.ii: the regions of high and low pressure in a sound wave are called compressions and rarefactions, respectively. High pressure is the compression, which is the peak of the plot.
(c) Two things are wrong. First, the plot's vertical axis is pressure, not position, so the curve is a graph and not the shape of anything. Second, and this is the substance, the wave is longitudinal, so by 14.1.A.5 the air moves parallel to the direction the sound travels, back and forth along the beam, never across it.
A cleaner way to say it: the peaks of the plot are places where the air is crowded, at $0.500\ \text{m}$ intervals along the beam, and between them at $0.250\ \text{m}$ offsets the air is spread out. Every molecule oscillates along the same line the sound is running down, through a distance far smaller than the $0.500\ \text{m}$ wavelength.

(a) $\lambda = 0.500\ \text{m}$ . (b) Compression to compression is $0.500\ \text{m}$ ; compression to the nearest rarefaction is $0.250\ \text{m}$ . (c) The curve is a pressure graph, not a shape, and the air moves parallel to the direction of travel because sound is longitudinal (14.1.A.5 and 14.1.A.5.i).

Which of these can be polarized, and how you justify it

Four waves are sent, one at a time, through a polarizing filter and then through a second identical filter turned ninety degrees to the first: a laser beam, a $686\ \text{Hz}$ tone from a loudspeaker, a wave on a taut rope, and a compression pulse sent along a stretched spring. For each, state whether the arrangement can stop it, and justify the answer from the CED.

Start from the single test. 14.3.A.2.i says transverse waves can be polarized and oscillate in a single plane. 14.3.A.2.ii says longitudinal waves cannot be polarized. So the question 'can this be polarized?' reduces to 'is this transverse?', which reduces to 14.1.A.4 against 14.1.A.5: is the disturbance perpendicular to the travel, or parallel to it?
Laser beam. An electromagnetic wave, and Topic 14.4 states that the electric and magnetic field oscillations are perpendicular to the direction of propagation, so it is transverse. The first filter leaves it oscillating in a single plane; the second passes only the perpendicular plane, so for ideal filters nothing gets through. Stopped.
$686\ \text{Hz}$ tone. 14.1.A.5.i says sound waves are modeled as mechanical longitudinal waves. The air's motion is already confined to one line, the line of travel, so there is no set of orientations for a filter to choose among. Not stopped, and not even dimmed by this mechanism.
Wave on a taut rope. The rope moves across the direction the wave runs, so it is transverse by 14.1.A.4. A slot lets through only the component of the rope's motion aligned with it, and a second slot at ninety degrees blocks what is left. Stopped. Note that this one is mechanical, so the CED's transverse and longitudinal classification is not the same thing as its mechanical and electromagnetic classification in 14.1.A.2.
Compression pulse along a spring. The coils move along the spring's own length, parallel to the travel, so it is longitudinal by 14.1.A.5. Not stopped, for exactly the reason sound is not.
Two cautions on wording. The CED says a transverse wave that is reflected, refracted, or passed through specific openings may be polarized, so 'may' rather than 'is'. And 14.3.A.3 only says polarization may result in a reduction of the wave's intensity; the AP Physics 2 sheet prints no equation for how much, so a numerical fraction has to come from the question.

The laser beam and the rope wave can be stopped, because both are transverse and can be polarized (14.3.A.2.i). The sound and the spring compression cannot, because both are longitudinal (14.3.A.2.ii and 14.1.A.5.i). The dividing line is transverse against longitudinal, not electromagnetic against mechanical: the rope wave is mechanical and still polarizes.

Frequently asked questions

What is the difference between a transverse and a longitudinal wave?

The direction of the disturbance relative to the direction the wave travels. AP Physics 2 essential knowledge 14.1.A.4 says that in a transverse wave the direction of the disturbance is perpendicular to the direction of propagation, and 14.1.A.5 says that in a longitudinal wave it is parallel to the direction of propagation. Everything else follows from that one comparison: crests and troughs against compressions and rarefactions, and above all the fact that only transverse waves can be polarized.

Is sound transverse or longitudinal?

Longitudinal. AP Physics 2 essential knowledge 14.1.A.5.i states that sound waves are modeled as mechanical longitudinal waves. Air molecules move back and forth along the direction the sound is travelling, not across it, and the regions of high and low pressure that result are called compressions and rarefactions, which is 14.1.A.5.ii. Drawings of sound as a sine curve are graphs of pressure against position, not pictures of a wavy medium.

Why can only transverse waves be polarized?

Because perpendicular leaves a choice of direction and parallel does not. In a transverse wave the disturbance is perpendicular to the travel, and perpendicular is a whole plane of possible orientations, so a filter can select one of them and leave the wave oscillating in a single plane. That is AP Physics 2 essential knowledge 14.3.A.2.i. In a longitudinal wave the disturbance is parallel to the travel, which is a single line, so there is nothing to select and nothing to filter. Essential knowledge 14.3.A.2.ii states flatly that longitudinal waves cannot be polarized.

Is light transverse or longitudinal?

Transverse. Light is an electromagnetic wave, and AP Physics 2 Topic 14.4 states that electromagnetic waves are transverse because the oscillations of the electric and magnetic fields are perpendicular to the direction of propagation. That is exactly why light can be polarized while sound cannot. Note that transverse and electromagnetic are two separate classifications: a wave on a string is transverse and mechanical, so it can be polarized and it still needs a medium.

What are compressions and rarefactions?

They are the two extremes of a longitudinal wave, and AP Physics 2 essential knowledge 14.1.A.5.ii names them in order: the regions of high and low pressure in a sound wave are called compressions and rarefactions, respectively. So a compression is where the medium is crowded together and the pressure is above equilibrium, and a rarefaction is where it is spread out and the pressure is below equilibrium. Adjacent compressions are one wavelength apart, and a compression to the nearest rarefaction is half a wavelength.

Do transverse and longitudinal waves obey different equations?

No. Both obey the printed relationship between wavelength, speed and frequency, both have their speed set by the type of wave and the properties of the medium under essential knowledge 14.1.A.3, both reflect and transmit at a boundary while keeping their frequency, and both superpose by adding displacements, which gives both of them interference, beats and standing waves. Polarization is the one behavior that separates them. That shared arithmetic is why the distinction is easy to overlook right up to the point a question asks about a filter.

Can a single medium carry both transverse and longitudinal waves?

Yes, and a slinky is the standard demonstration: shake it sideways for a transverse wave, push and pull it along its length for a longitudinal one. The two usually travel at different speeds, which is consistent with AP Physics 2 essential knowledge 14.1.A.3, since that statement makes the speed depend on the type of wave as well as on the properties of the medium. The classification describes the wave, not the material it is in.