Wave Basics

The video lesson for this topic is coming soon.

Essential Question

What is a wave, and what does it carry?

Ripples on a pond, sound from a speaker, and light from the Sun are all waves. By the end of this lesson, you should be able to explain what a wave carries, tell transverse and longitudinal waves apart, and label the parts of a wave.

What Is a Wave?

A disturbance that moves
Carries energy
Matter stays in place

A blue wave on water with a red cork sitting on a crest. A small red double arrow above the cork shows it bobbing up and down. A long blue arrow below points right, labeled energy travels this way. Caption: the wave moves on, the cork stays put.

A wave is a disturbance that travels from place to place. When a ripple passes a floating cork, the cork bobs up and down, but it does not ride along with the wave. The water mostly stays where it is. What actually travels is energy. A wave carries energy, not matter.

Mechanical vs. Electromagnetic

Mechanical waves need a medium
Medium: the stuff that waves
EM waves can cross empty space

Two cards. A pink card reads: Mechanical, needs a medium, examples sound, water waves, and rope waves. A cyan card reads: Electromagnetic, no medium needed, examples light, radio, and X-rays. Caption: sunlight crosses empty space.

Mechanical waves need a medium, the material the wave travels through. Sound travels through air, water waves travel through water, and rope waves travel along a rope. Without a medium, there is no mechanical wave, which is why there is no sound in space. Electromagnetic (EM) waves, like light and radio, do not need a medium. Sunlight crosses about 150 million kilometers of nearly empty space to reach Earth.

Transverse Waves

Particles move perpendicular to the wave
Like flicking a rope up and down
Light is transverse

A blue sine wave on a rope. A red dot on the rope has a vertical red double arrow labeled particle motion. A blue arrow below points right, labeled wave motion. Caption: transverse, motion is perpendicular to the wave.

In a transverse wave, the particles of the medium move perpendicular (at right angles) to the direction the wave travels. If you flick a rope up and down, each bit of rope moves up and down while the wave travels sideways along the rope. Light and other EM waves are transverse.

Longitudinal Waves

Particles move parallel to the wave
Compressions and rarefactions
Sound is longitudinal

A row of vertical blue lines like a stretched spring. Some lines are bunched together, labeled compression, and some are spread apart, labeled rarefaction. A red double arrow pointing left and right is labeled particle motion, and a blue arrow pointing right is labeled wave motion. Caption: longitudinal, parallel motion.

In a longitudinal wave, the particles of the medium move back and forth parallel to the direction the wave travels. Push and pull one end of a spring toy and you’ll see crowded regions called compressions and stretched-out regions called rarefactions travel down the spring. Sound is a longitudinal wave: air molecules are squeezed together and spread apart as the sound passes.

Parts of a Transverse Wave

Crest: the highest point
Trough: the lowest point
Equilibrium: the rest position

A blue sine wave drawn over a dashed gray horizontal line labeled equilibrium. A top point of the wave is labeled crest and a bottom point is labeled trough. Caption: crest on top, trough on the bottom.

Every transverse wave has the same basic parts. The crest is the highest point of the wave, and the trough is the lowest point. The equilibrium line is where the medium would sit if there were no wave at all. A wave swings above and below its equilibrium line.

Amplitude and Wavelength

Amplitude A: equilibrium to crest
Wavelength λ: one full cycle
Measure λ crest to crest

A blue sine wave over a dashed equilibrium line. A black double arrow above the wave runs from one crest to the next crest, labeled wavelength lambda. A red double arrow at the right runs from the equilibrium line up to the height of a crest, labeled A for amplitude. Caption: lambda is crest to crest, A is rest line to crest.

The amplitude (A) is the distance from the equilibrium line to a crest (or to a trough). It is not the distance from crest to trough. The wavelength (λ, the Greek letter lambda) is the length of one full cycle of the wave, measured from one crest to the next crest, or from one trough to the next trough. Wavelength is a length, so it is measured in meters.

Amplitude and Energy

Bigger amplitude, more energy
Loud sounds: big amplitude
Tall ocean waves: big amplitude

Two blue waves with the same wavelength. The top wave has a small amplitude, labeled small A, less energy. The bottom wave has a large amplitude, labeled big A, more energy.

The bigger the amplitude, the more energy the wave carries. A gentle ripple has a small amplitude and little energy, while a storm wave that can knock you over has a large amplitude. For sound, a larger amplitude means a louder sound. Notice that the two waves here have the same wavelength. Amplitude and wavelength are separate properties.

Worked Examples

Try each problem on your own first, then check your work against the solution.

Example 1: Reading a Wave Graph

The graph shows a wave on a rope. The crests reach 3 cm above equilibrium at 0.5 m, 2.5 m, and 4.5 m. Find the amplitude and the wavelength.

A graph of rope displacement in centimeters, from negative 4 to 4, versus position in meters, from 0 to 6, with grid lines. A blue sine wave starts at 0, reaches crests of 3 cm at 0.5 m, 2.5 m, and 4.5 m, and troughs of negative 3 cm at 1.5 m, 3.5 m, and 5.5 m.

Amplitude: read the height of a crest above the equilibrium line (0 cm): A = 3 cm
Wavelength: find two neighboring crests: 0.5 m and 2.5 m
Subtract: λ = 2.5 m − 0.5 m
Answer: λ = 2.0 m

You could also measure trough to trough (1.5 m to 3.5 m) and get the same wavelength.

Example 2: Counting Wavelengths

A wave on a rope shows exactly 3 full wavelengths along a 4.5 m section. What is the wavelength?

A blue wave with exactly three full cycles drawn above a double arrow labeled 4.5 m.

Knowns: 3 wavelengths fit in 4.5 m
Equation: λ = total length ÷ number of wavelengths
Substitute: λ = 4.5 m ÷ 3
Answer: λ = 1.5 m

Example 3: Crest to Trough

A boat rides over ocean waves. It moves 1.2 m from the top of a crest to the bottom of a trough. What is the amplitude of the waves?

A blue ocean wave with a dashed equilibrium line. A black double arrow runs from the height of a crest down to the depth of a trough, labeled 1.2 m.

Knowns: crest to trough = 1.2 m
Relationship: crest to trough is two amplitudes: one above equilibrium and one below
Substitute: A = 1.2 m ÷ 2
Answer: A = 0.60 m

Common mistake: answering 1.2 m. Amplitude is measured from equilibrium, not from crest to trough.

Example 4: The Stadium Wave

Fans do “the wave”: each person stands up and sits down as the wave travels around the stadium. Is it transverse or longitudinal? Does any fan travel around the stadium?

A row of seven stick-figure fans behind a stadium wall. The fan in the middle is standing all the way up, the fans next to him are half standing, and the fans on the ends are seated. A blue arrow below points right, labeled wave moves.

Fan motion: each fan moves up and down
Wave motion: the wave travels sideways around the stadium
Compare: up and down is perpendicular to sideways
Answer: transverse. No fan travels around the stadium. Each fan stays in their seat. Only the energy (the disturbance) travels.

Big Ideas

Waves carry energy, not matter
Mechanical waves need a medium; EM waves don’t
Transverse: perpendicular. Longitudinal: parallel
λ: crest to crest. Bigger A, more energy

Back to the essential question: a wave is a disturbance that carries energy from one place to another without carrying matter along with it. Waves can be transverse or longitudinal, and bigger amplitude means more energy. Next up, we’ll measure how often waves repeat and how fast they travel in Frequency, Period, and Wave Speed.