The big ideaA wave is energy traveling through a medium (or, for light, through nothing at all) without the medium's own particles traveling along with it. This lesson builds the vocabulary — pulse, medium, transverse, longitudinal, wavelength, amplitude, frequency, period — that the rest of the module runs on, then asks you to apply it in a discussion post.
The one sentence to hold onto for the whole module
Almost every confusing wave question comes back to mixing up the wave with what it's made of. Settle this once and the vocabulary in this lesson stops being a memorization exercise.
Not sure about the basics underneath this lesson?
1
Energy travels. Matter doesn't (much).
Watch a flag rippling in the wind. The ripple clearly moves down the flag, fast. But no thread of fabric travels from the pole to the far end, each bit of cloth just flaps up and down where it already is. That ripple is a wave. Same story for every wave in this lesson.
2
Two boxes: does it need a medium?
Sort anything wave-like into one of two boxes. Mechanical (needs stuff to travel through: sound, water, a rope, a slinky). Electromagnetic (light and its relatives; can cross empty space). If you're ever unsure which box something's in, ask: could this cross a total vacuum? Only light-family waves can.
3
Transverse vs. longitudinal, with your own hand
Wiggle a jump rope up and down while your friend holds the other end: the wave travels toward your friend (sideways), but your hand moves up and down (crosswise). That's transverse. Now push and pull a spring toward your friend instead: your hand moves back and forth along the same line the wave travels. That's longitudinal. Sound in air works like the spring.
Optional interactive:PhET Wave on a String makes amplitude, frequency, and wavelength visible. It models a transverse string, so do not use its shape as a model for longitudinal sound.
Got it now? Scroll back up and re-read the section — it should land differently.
A wave moves energy, not matter
Hold one end of a rope while a friend holds the other, then jerk your end down and back up once. A single hump, called a pulse, travels down the rope to your friend. Keep doing it rhythmically and you get a continuous wave: a repeating disturbance that carries energy from one place to another. The rope itself is the medium, the material that carries the disturbance. The key idea, worth remembering all the way through this module: a wave transports energy, not matter. Each piece of rope moves up and down in place and hands the disturbance to its neighbor; no single piece of rope travels from your hand to your friend's.
Mechanical waves need a medium; light doesn't
Most waves need a medium to travel through: sound needs air (or water, or a wall), a rope wave needs the rope, an ocean wave needs water. These are mechanical waves. Electromagnetic waves — visible light, radio, microwaves, X-rays — are the exception. They can travel through empty space with no medium at all, which is how sunlight reaches Earth across the vacuum between the Sun and us. They can also travel through some media (light through glass or water), but they don't require one.
Transverse waves: the anatomy of a wave
In a transverse wave, particles of the medium oscillate perpendicular to the direction the wave travels. Picture the stadium wave at a football game: the wave itself moves sideways around the stadium while each person only moves up and then back down. A rope wave and light are both transverse.
The crest is a wave's highest point; the trough is its lowest point. Wavelength (λ) is the distance from one crest to the next (or trough to trough), measured in meters. Amplitude is the maximum distance the wave moves away from its resting position, the equilibrium line — think of amplitude as how big the wave is, not how long it is.
Not sure about this bit?
This is a labeling exercise more than a hard concept. Once you can point to each part on any wave picture, the rest of the module gets much easier.
1
Crest and trough are just highest and lowest
Crest = the top of the hump. Trough = the bottom of the dip. That's it, no trick to it.
2
Amplitude is a height, not a length
Amplitude measures up-and-down from the resting middle line to a crest (or down to a trough). It tells you how big or energetic the wave is, not how long one cycle is.
3
Wavelength is a length, not a height
Wavelength measures sideways, crest to crest (or trough to trough, or any two matching points one full cycle apart). Mixing up amplitude and wavelength is the single most common labeling mistake.
Got it now? Scroll back up and re-read the section — it should land differently.
Frequency and period
Frequency (f) is how many complete waves pass a point each second, measured in hertz (Hz), which means cycles per second. Period (T) is the time in seconds for one complete wave to pass, so frequency and period are reciprocals of each other.
Period–frequency relationship
Period from frequency
T=f1​
T in seconds, f in hertz (Hz).
Frequency from period
f=T1​
A wave with a short period repeats often, so it has a high frequency.
Wavelength and frequency trade off at a fixed speed
For a wave moving at a fixed speed (like sound in a given room, or light in a vacuum), wavelength and frequency move opposite to each other: shrink the wavelength and the frequency has to rise to keep the same speed, since v = fλ (used with numbers starting in 05.03). The diagram below shows two waves of the same speed side by side: the top one is packed with short wavelengths, so more of them pass a point each second (higher frequency); the bottom one is stretched into long wavelengths, so fewer pass each second (lower frequency).
Longitudinal waves: compression and rarefaction
In a longitudinal wave, particles oscillate parallel to the direction the wave travels, back and forth along the same line the energy is moving, instead of up and down across it. Sound is the everyday example: a speaker cone pushes air molecules forward, then pulls back, over and over.
A compression is a region where the medium's particles are bunched close together (high density). A rarefaction is a region where they're spread apart (low density). Because a longitudinal wave has no crest or trough to measure between, its wavelength is measured compression-to-compression or rarefaction-to-rarefaction instead.
Not sure about this bit?
Sound is the wave you already have the most experience with, so use that.
1
Compression = squeeze, rarefaction = stretch
Every time a speaker cone pushes forward, it squeezes the air in front of it into a compression. Every time it pulls back, it leaves a rarefaction, a thinned-out region, behind. Those regions travel outward one after another.
2
No crest, so measure differently
A longitudinal wave doesn't have a hump to point to, so wavelength is measured compression-to-compression instead of crest-to-crest. Same idea, different landmark.
Got it now? Scroll back up and re-read the section — it should land differently.
Tsunamis: an unusually long wave
A tsunami is an ocean wave with an extremely long wavelength, sometimes over 200 km, caused by an earthquake, underwater landslide, or volcanic eruption that suddenly shifts a large amount of water. In the open ocean a tsunami can travel over 900 km/hr and be barely noticeable, since its height there may be under a meter spread across such a long wavelength. A normal wind-driven wave only travels around 90 km/hr and mostly moves water in circles rather than covering distance. As a tsunami reaches shallow water near shore, its speed drops and its height grows rapidly, sometimes to 15 m or more. Everything about it is still governed by the same wave definitions above; it's simply a wave with a wavelength and period far outside everyday experience.
Task-fit practice
These check whether you'd catch a mislabeled wave diagram or a mixed-up term, the same kind of thing a discussion reader would notice.
