What a Wave Is - Physics for Pilot Assessments

A wave is how energy gets from one place to another without anything being carried along with it. That sentence is doing more work than it looks, and unpacking it is the business of this lesson. By the end of it you should be able to say what does and does not travel when a wave passes, measure an amplitude and a wavelength on a diagram without swapping them over, define frequency and period and convert between them in both directions, and tell a transverse wave from a longitudinal one.

Energy travels; the material stays put

Tie one end of a long rope to a post, hold the other end, and flick your wrist once. A hump runs along the rope to the far end, and if there were a bell hanging on the post the hump could ring it — so energy has plainly travelled from your hand to the post. But the rope has not travelled. Each bit of it moved up and then back down as the hump went past, ending exactly where it began, and no piece of rope arrived at the post that was not already there. That is the defining feature of a wave: the disturbance moves, along with the energy it carries, while the material it moves through only oscillates about its old position and stays where it was.

The same distinction works on water. A cork floating on a pond bobs up and down as ripples pass under it and does not get carried across; that is why waves at sea lift a boat rather than sweep it away, and why a leaf on a pond stays roughly put no matter how many ripples pass. Contrast that with a thrown stone, where the matter itself makes the whole journey. Both deliver energy, but only one delivers matter — and the word for the material a wave passes through, whether rope, water, air or steel, is the medium. Keep the two halves of the definition together: a wave transfers energy without transferring matter.

Two ways for a wave to be built

Waves differ in the direction the material moves compared with the direction the wave travels, and there are exactly two options. In a transverse wave the material moves at right angles — across — the direction of travel: the rope wave is transverse, because your hand moved up and down while the hump moved horizontally along the rope, and water ripples are transverse in the same way. In a longitudinal wave the material moves along the same line the wave is travelling, backwards and forwards rather than side to side. Push and pull the end of a long spring and you can see it: a region where the coils are squeezed together runs along the spring, each coil moving briefly forwards and back along the spring's own direction.

Because the material in a longitudinal wave moves along the direction of travel, what runs along the medium is not a hump but a pattern of crowding: regions where the material is momentarily squeezed closer together and, in between, regions where it is momentarily spread out. A squeezed region is called a compression and a spread-out region a rarefaction. Sound is the important example, and the next lesson but one deals with it properly; for now what matters is that not every wave is transverse, and that the picture of a wave as a wiggly line — however useful — is a graph of displacement rather than a photograph, when the wave in question is longitudinal.

Every wave word is a distance on this picture. Amplitude is measured from the undisturbed middle line to a crest, never from crest to trough, and wavelength runs from one crest to the next — or, in the longitudinal wave below, from one compression to the next. In a transverse wave the material moves across the direction of travel; in a longitudinal wave it moves back and forth along it.

Amplitude

The amplitude of a wave is the greatest distance the material moves away from its undisturbed position — the height of a crest measured from the middle line, not from the trough. That qualification is the whole of the first trap in this topic: the distance from the top of a crest to the bottom of a trough is twice the amplitude, and it is offered as the amplitude in more or less every item that shows a diagram. On a rope wave the amplitude is measured in metres, like any other displacement, and on a longitudinal wave it is how far each particle shifts back and forth along the line of travel.

Amplitude matters because it is what carries the energy. A bigger flick of the wrist puts more energy into a rope, and the wave that results has taller crests and deeper troughs but is otherwise identical — the same length of hump, arriving at the same rate. So amplitude is independent of everything else about a wave, and it is the quantity to look at when a question asks about the energy a wave carries, how loud a sound is, or how bright a light is.

Wavelength

A wave repeats. Follow a snapshot of a rope wave along its length and the same shape comes round again and again, and the wavelength is the distance over which it repeats once — most easily measured from one crest to the next crest, though from any point to the matching point on the next repeat gives the same answer, trough to trough included. For a longitudinal wave it is the distance from one compression to the next. It is a distance, so it is measured in metres, and it is written with the Greek letter lambda, λ, which looks like an upside-down y.

Wavelengths in the real world span an absurd range, which is why the prefixes matter. Ocean swell runs to hundreds of metres, audible sound covers roughly two centimetres to seventeen metres, and visible light is a few hundred nanometres, a nanometre being a thousand-millionth of a metre. Nothing in this module asks you to calculate with wavelengths that small; what it does ask is that you never confuse a wavelength with an amplitude, since one is measured along the wave and the other across it.

Frequency, and the hertz

Stop looking at a snapshot and stand at one point instead, counting crests as they arrive. The frequency of a wave is the number of complete cycles that pass a fixed point each second — equivalently, for the source, the number of complete oscillations it makes each second. The unit is the hertz, written Hz, and one hertz is one cycle per second, so a wave at 5 hertz sends five crests past you every second. Since the counts get large, the prefixes reappear: a kilohertz is a thousand hertz, a megahertz is a million, and a gigahertz is a thousand million.

Frequency is set by whatever is making the wave, and it does not change just because the wave has moved into a different material. That is a fact to hold on to, because it becomes important in the next lesson: shake a rope faster and you get more crests per second, and nothing that happens along the rope can add crests or take them away.

Period, and why it is frequency upside down

The period of a wave is the time taken for one complete cycle to pass — the time from one crest to the next arriving at the same point. It is a time, measured in seconds, and it is written with a capital T. Period and frequency are two ways of describing the same thing, and each is the reciprocal of the other, meaning one divided by it. The logic is worth doing once rather than memorising: if five complete cycles pass every second, then each one takes a fifth of a second, so the period is 1 divided by 5. In general the period is 1 divided by the frequency, and turning it round, the frequency is 1 divided by the period.

Period and frequency

T = \frac{1}{f}

$T$: the period — the time for one complete cycle, in seconds (s)
$f$: the frequency — cycles per second, in hertz (Hz)
$1$: one cycle, which is what the period is the time for

The same statement rearranged gives $f = \frac{1}{T}$ , and you should read that as one relationship rather than two: multiply both sides of $T = \frac{1}{f}$ by f and you get Tf = 1, which can be divided by either letter to isolate the other. A useful consequence to notice is that they run in opposite directions — a high frequency means a short period, and a low frequency a long one — so if you calculate a period of 20 seconds for a wave at 50 hertz, you have divided the wrong way round.

Example 3 — counting, then converting

A buoy is lifted by 30 complete waves in one minute. What is the frequency of the waves, and what is their period? If the buoy rises 1.5 metres from the flat-water level at each crest, what is the amplitude?

Frequency is cycles per second, so convert the minute first: one minute is 60 seconds.
30 cycles in 60 seconds is $\frac{30}{60} = 0.5$ cycles per second, so the frequency is 0.5 hertz. A frequency below 1 hertz is nothing strange — it just means each cycle takes longer than a second.
The period is $\frac{1}{0.5} = 2$ seconds, which fits the picture: one wave lifting the buoy every two seconds.
The amplitude is the displacement from the undisturbed position, and the flat-water level is that position, so the amplitude is 1.5 metres.
Note the distractor built into the last part: the buoy travels 3 metres in total between the bottom of a trough and the top of a crest, and that figure is twice the amplitude.

Why it matters in aviation

Almost everything a crew uses to talk to anyone or to know where it is arrives as a wave. A controller's voice reaches the flight deck as a pattern impressed on a radio carrier: nothing material crosses the gap, only the disturbance and the energy it carries, which is why a transmission from far away arrives just as promptly as one from the aircraft alongside. Distance measurement works the same way from the other end — a pulse goes out, part of it comes back from whatever it met, a cloud ahead or the ground below, and the time the round trip took gives the range, because the speed of the wave is known.

Position from satellites is the same idea again, worked out from when signals sent by several distant transmitters arrive. In every one of these cases the quantity that carries the information is a property of the wave — its timing, its frequency, the pattern imposed on it — and not of any matter delivered along with it. Keeping the wave and the medium separate in your head is what makes the whole arrangement intelligible rather than magical.

What the test asks

Two swaps and one assumption. The first swap is amplitude for wavelength, usually on a labelled diagram where the two arrows are both present and the wrong one is offered — remember that wavelength runs along the wave and amplitude across it. The second swap is crest-to-trough for amplitude, which gives exactly double the right answer, so if your answer is twice one of the options, check where you measured from. The assumption is that every wave is transverse: an item asks which of a list is longitudinal, and the reliable trap is choosing something visibly wiggly, when the answer is sound, because sound travels as compressions and rarefactions along its direction of travel. Expect too a period-and-frequency item where the trap is to hand back the number unchanged with the unit swapped from hertz to seconds, which is only correct for the one wave whose frequency happens to be 1 hertz.