Waves are one of the great unifying ideas in physics: the same handful of concepts — wavelength, frequency, period, speed — describe everything from ripples on a pond to the light arriving from a galaxy billions of light years away. This workbook builds the wave "toolkit" from the ground up, then puts it to work on two very different kinds of wave: sound and light. It finishes by asking what happens when a wave reaches a boundary. The other three workbooks in this set (Velocity Change, Interference, Standing Waves) build directly on what you learn here.
By the end of this workbook you should be able to:
Describe waves as transverse or longitudinal, and use a simple particle/spring model to explain how each type transfers energy without transferring matter.
Define and apply wavelength λ, frequency ƒ, time period T and wave speed v, including v = ƒλ = λ/T.
Explain the nature of sound waves as a longitudinal mechanical wave, and relate pitch and loudness to frequency and amplitude.
Explain the nature of electromagnetic waves as transverse oscillations of electric and magnetic fields that require no medium, and describe the electromagnetic spectrum.
Compare and contrast mechanical waves and electromagnetic waves.
Describe waves travelling in two and three dimensions using wavefronts and rays.
Apply the law of reflection to rays and to wavefronts at a boundary, and explain the difference between reflective and non-reflective surfaces.
1. What is a wave?
Drop a pebble into a still pond and rings of ripples spread outward from the splash. Shake one end of a rope and a "wiggle" travels along it to the other end. In both cases, something is clearly moving away from the source — but it is not the water itself, and it is not the rope itself. A cork floating on the pond bobs up and down as the ripple passes but ends up back where it started; a piece of tape on the rope oscillates side to side but travels nowhere. What actually moves outward is energy.
Key idea. A travelling (or progressive) wave is an oscillating disturbance that transfers energy away from a source, through a medium or through space, without any net transfer of the matter of the medium itself.
Fig. 1.1 A wave created by continuously shaking one end of a rope. Energy travels from A to B; each point on the rope (such as P) simply oscillates about a fixed position.
The substance through which a mechanical wave travels — air, water, a rope, the ground — is called the medium. Not every wave needs one.
Mechanical waves
Electromagnetic waves
What is oscillating?
particles of a physical medium
electric and magnetic fields
Needs a medium?
yes
no — can cross a vacuum
Examples
sound, water waves, waves on a string, seismic (earthquake) waves
light, radio waves, X-rays, gamma rays
Sections 5-7 return to this distinction in much more depth.
Worth remembering
A very common error is to think a wave carries the medium along with it. It doesn't. A gull floating on the sea rises and falls as waves pass beneath it, but it isn't swept out to sea by every wave — the water (and the gull) mostly stays put; only the disturbance, and the energy it carries, moves on.
Check your understanding
1A cork floats on the surface of a pond. A single circular ripple wave, produced by a dropped pebble, passes underneath it. Describe the motion of the cork while the ripple passes, and state whether the cork ends up further from the point where the pebble landed.
The cork bobs up and down (oscillates vertically) about its original position as the ripple passes, then returns to rest. It does not end up further from the splash — only the disturbance (and the energy associated with it) travels outward, not the water or anything floating on it.
2State two examples of mechanical waves and one example of an electromagnetic wave. For one of your mechanical examples, identify the medium through which it travels.
Any two of: sound, water waves, waves on a string/rope, seismic waves (mechanical); any one of: light, radio waves, microwaves, X-rays, gamma rays (electromagnetic). Example medium: sound travels through air (or water, or a solid).
3Explain, in terms of energy and matter, why a wave is different from simply throwing an object (like a ball) from A to B.
Throwing a ball transfers energy from A to B by physically moving matter (the ball) from A to B. A wave transfers energy from A to B without any net transfer of matter — the particles of the medium (or, for an EM wave, the fields) merely oscillate about fixed positions as the disturbance and its energy pass through.
2. Transverse and longitudinal waves
It helps to picture a mechanical medium as a long line of small masses, each connected to its neighbours by springs (representing the internal forces that pull a disturbed particle back towards its neighbours). If you shake the end of this chain, there are exactly two independent ways to do it: shake it side to side, or shake it back and forth along its length. These two choices produce the two fundamental families of mechanical wave.
Transverse wave. Each particle of the medium oscillates perpendicular to the direction in which the wave transfers energy.
Longitudinal wave. Each particle of the medium oscillates parallel to the direction in which the wave transfers energy.
Fig. 2.1 In a transverse wave, particles move perpendicular to the direction of energy transfer, producing crests and troughs. In a longitudinal wave, particles move parallel to it, producing regions of compression (particles closer together) and rarefaction (particles further apart).
Crest / trough: the highest / lowest point of a transverse wave. Compression / rarefaction: a region of increased / decreased particle density (and pressure) in a longitudinal wave.
Live simulation: watch the particles move
Transverse vs. longitudinal
Watch one highlighted particle (in amber). In transverse mode it moves up/down; in longitudinal mode it moves left/right, bunching up with its neighbours to form compressions.
Fig. 2.2 The same wave energy, moving left to right, drawn two ways. Toggle the mode and watch how an individual particle's motion differs.
Check your understanding
4Seismologists classify earthquake waves as P-waves (primary) or S-waves (secondary). P-waves are longitudinal and travel through both solids and liquids; S-waves are transverse and can only travel through solids. Explain, in terms of particle motion, why a transverse wave cannot travel through a liquid, while a longitudinal wave can.
A transverse wave needs the medium to resist being sheared sideways (i.e. it needs a restoring force when particles are displaced perpendicular to the direction of travel) — liquids (and gases) flow freely and don't resist this sideways shearing, so they cannot support a transverse wave. A longitudinal wave only needs the medium to resist being compressed, which liquids (and gases) do, so longitudinal waves can travel through them.
5A "slinky" spring lying on a table is given a single sharp push along its length. Describe what you would see travel along the spring, and state the type of wave this represents.
A single region where the coils are pushed closer together (a compression) travels along the spring, followed by the coils returning to their normal spacing. This is a longitudinal pulse.
6Using the simulation above, switch between transverse and longitudinal mode at the same frequency. In your own words, describe one similarity and one difference between the two particle motions you observe.
This is a descriptive, simulation-based question. Similarity: in both modes each particle oscillates back and forth about a fixed rest position at the same frequency, and neighbouring particles are slightly out of phase with each other, which is what makes the pattern appear to travel. Difference: in transverse mode the oscillation is vertical (perpendicular to the direction of travel), producing crests/troughs, while in longitudinal mode it is horizontal (parallel to the direction of travel), producing compressions/rarefactions.
3. Describing a wave: wavelength, amplitude, period
Whatever kind of wave we're dealing with, the same small set of quantities describes it completely.
Key definitions.
Wavelength, λ — the shortest distance between two points on a wave that are oscillating in phase (e.g. crest to crest, or compression to compression). Unit: metre (m).
Amplitude — the maximum displacement of a particle of the medium from its equilibrium (rest) position.
Time period, T — the time taken for one complete oscillation of a particle, or equivalently the time for one full wavelength to pass a fixed point. Unit: second (s).
Frequency, ƒ — the number of complete oscillations per second, or the number of wavelengths passing a fixed point per second. Unit: hertz (Hz). ƒ = 1/T.
Fig. 3.1 The same sinusoidal shape can represent two different things: a photograph of the whole wave at one instant (left, wavelength read off the x-axis), or a video of one single particle over time (right, period read off the x-axis).
Common mistake
Both graphs above can represent either a transverse or a longitudinal wave — the vertical axis is "displacement," which for a longitudinal wave means displacement along the direction of travel, not up/down in real space. Don't assume a sine-shaped graph automatically means a transverse wave.
Pulse: a single, short-duration wave disturbance (not a continuous, repeating wave) — for example, one clap, or one flick of a rope.
Live simulation: phase, progressive and stationary waves
This tool visualises how neighbouring particles on a wave are out of phase with each other by a varying amount — the same "shortest distance between two points moving in phase" idea behind the definition of wavelength above. It also lets you compare this progressive (travelling) wave against a stationary (standing) wave, which you'll meet properly in the Standing Waves workbook later in this set — for now, focus on the progressive wave view and how the phase difference between two points changes smoothly with their separation.
Interactive simulation — open the online version of this workbook to launch it.
Simulation by Dr Dan Jones (drjonesphysics.com). If the embedded version above doesn't load, open it directly in a new tab via that link.
Check your understanding
7A transverse wave has a period of 0.40 s. Calculate its frequency.
ƒ = 1/T = 1/0.40 = 2.5 Hz.
8Sketch a displacement–time graph for a transverse wave of amplitude 3.0 cm and period 2.0 s, assuming the particle starts (at t = 0) at its maximum positive displacement. Continue your sketch for a duration of 6.0 s.
A cosine-shaped curve starting at +3.0 cm at t = 0, crossing zero at t = 0.5 s, reaching −3.0 cm at t = 1.0 s, back to zero at t = 1.5 s, and +3.0 cm again at t = 2.0 s — repeating this full cycle three times over the 6.0 s shown (three complete periods).
9A longitudinal sound pulse is produced by a single hand-clap. Explain, using the term "pulse" correctly, why this is different from the sound produced by a continuously ringing bell.
A hand-clap produces a single, short-duration disturbance — a pulse — with no repeating pattern. A continuously ringing bell produces a repeating, periodic disturbance with a well-defined wavelength, period and frequency, i.e. a continuous travelling wave rather than a single pulse.
4. Wave speed: v = ƒλ = λ/T
Every time period T, a wave advances forward by exactly one wavelength λ (that's what "period" and "wavelength" mean, put together). Speed is distance divided by time, so:
wave speed, v = λ / T
Since frequency and period are reciprocals (ƒ = 1/T), this can equally be written as:
v = ƒλ (or, combining both forms: v = ƒλ = λ/T)
Key idea. v, ƒ and λ are all properties of the wave itself, but v is set by the medium the wave is travelling through (its stiffness, density, temperature, etc.) — not by the source. If a wave crosses into a new medium, its speed and wavelength can change, but (as you'll see in Sections 5-6) its frequency, which is set by the source, generally stays the same.
Worked example 4.1
Ripples spread across a ripple tank. A stroboscope photograph shows 6 crests spread over a distance of 18.0 cm. A stopwatch shows that 25 ripples pass a fixed point in 10.0 s. Determine: (a) the wavelength, (b) the period, (c) the frequency, (d) the wave speed.
Answer:
a) 6 crests span 5 wavelength-gaps, so λ = 18.0 cm / 5 = 3.60 cm = 0.0360 m
b) T = 10.0 s / 25 = 0.400 s
c) ƒ = 1/T = 1/0.400 = 2.50 Hz
d) v = ƒλ = 2.50 × 0.0360 = 0.0900 m s⁻¹
Worked example 4.2
A loudspeaker emits a pure musical note of frequency 440 Hz (concert pitch A). The speed of sound in air is 340 m s⁻¹. Calculate the wavelength of this sound wave in air.
Answer:
v = ƒλ ⟹ λ = v/ƒ = 340/440 = 0.773 m
Live simulation: link λ, ƒ, T and v
v = ƒλ explorer
Frequency, ƒ = v/λ = …
Period, T = 1/ƒ = …
Fig. 4.1 Drag either slider and watch the wave animate at the resulting speed. Notice that ƒ and T are always calculated from λ and v — you can't set all four independently.
Optional extra — PhET: Wave on a String
Drive a string with an oscillator and directly control its frequency, amplitude, and damping.
Simulation: PhET Interactive Simulations, University of Colorado Boulder — phet.colorado.edu.
Check your understanding
10A radio station broadcasts at a frequency of 96.0 MHz. Radio waves travel at the speed of light, 3.00 × 10⁸ m s⁻¹. Calculate the wavelength of these radio waves.
λ = v/ƒ = (3.00×10⁸)/(96.0×10⁶) = 3.13 m.
11Water waves of wavelength 4.0 m travel at 2.0 m s⁻¹ towards a harbour wall. Determine the period and frequency of these waves, and state how many complete waves reach the wall in one minute.
T = λ/v = 4.0/2.0 = 2.0 s; ƒ = 1/T = 0.50 Hz; in 60 s, number of waves = ƒ × 60 = 30 waves.
12Two students each set up a wave with frequency 5.0 Hz on identical ripple tanks, but one tank contains deeper water than the other (waves travel faster in deeper water). Explain what will happen to the wavelength in the deeper tank compared with the shallower one.
Since v = ƒλ and ƒ is fixed by the source (the same in both tanks), a larger v in the deeper tank means a proportionally larger λ (λ = v/ƒ) — the wavelength will be longer in the deeper water.
13Using the simulation above, set λ = 1.0 m and v = 2.0 m s⁻¹. Read off the resulting frequency and period, then check your reading by calculating ƒ and T yourself from v = ƒλ.
ƒ = v/λ = 2.0/1.0 = 2.0 Hz; T = 1/ƒ = 0.50 s — this should match the simulation's live readout.
5. The nature of sound waves
Sound is a longitudinal mechanical wave. It is produced whenever a surface vibrates rapidly — a loudspeaker cone, a guitar string, human vocal cords — pushing the particles of the surrounding medium back and forth. Each push forward creates a brief region of higher pressure and particle density (a compression); each pull back creates a region of lower pressure and density (a rarefaction). This alternating pattern of compressions and rarefactions travels outward through the medium as sound.
Key idea. Because sound is a mechanical wave, it needs a medium — sound cannot travel through a vacuum. This is why, famously, "in space, no one can hear you scream": there are no air particles in the vacuum of space to compress and carry the disturbance.
The human ear can typically detect sound waves with frequencies from about 20 Hz to 20 kHz — the audible range. Frequencies above this range are called ultrasound; frequencies below it are called infrasound. Many animals (dogs, bats, dolphins) can hear well beyond the human range in one direction or the other.
Perceived quality
Physical wave property
Pitch (how "high" or "low" a note sounds)
frequency, ƒ
Loudness (volume)
amplitude (intensity ∝ amplitude²)
Speed of sound. Sound generally travels faster when the particles of the medium are closer together and the forces between them are stronger. This means sound usually travels fastest through solids, slower through liquids, and slowest through gases such as air. In air, the speed of sound also increases slightly as temperature rises (about 340 m s⁻¹ at room temperature), because warmer air molecules move — and collide, transmitting the disturbance — faster.
Extension: the decibel scale
Because the human ear can detect an enormous range of sound intensities, loudness is usually measured on a logarithmic scale, in decibels (dB), rather than a simple linear scale. Each extra 10 dB represents a sound that is 10× more intense — so a 70 dB sound (busy traffic) is 100× more intense than a 50 dB sound (quiet conversation), not just "20 more."
Optional extra — PhET: Sound Waves
Watch compressions and rarefactions spread out from a speaker in real time, and adjust frequency and amplitude.
Simulation: PhET Interactive Simulations, University of Colorado Boulder — phet.colorado.edu.
Check your understanding
14Explain why astronauts on a spacewalk cannot talk to each other directly (through the vacuum of space) and must instead use radio.
Speech is carried by sound, which is a mechanical (longitudinal) wave and needs a medium of particles to compress and transmit the disturbance. In the vacuum of space there is no medium, so sound cannot travel between the astronauts. Radio waves are electromagnetic and can travel through a vacuum, so they are used instead.
15Taking the speed of sound in air as 340 m s⁻¹, calculate the wavelength of sound at the two edges of the human audible range: 20 Hz and 20 000 Hz.
At 20 Hz: λ = 340/20 = 17 m. At 20 000 Hz: λ = 340/20000 = 0.017 m (1.7 cm).
16A student increases the volume of a musical note without changing which note is being played. State which property of the sound wave has changed, and which has stayed the same. Explain your reasoning.
The amplitude has increased (louder = more energy = larger amplitude); the frequency has stayed the same (the pitch/note is unchanged, and pitch is determined by frequency).
6. The nature of electromagnetic waves
Light behaves very differently from sound in one crucial respect: it reaches us from the Sun after crossing roughly 150 million kilometres of essentially empty space. There is no medium there for light to "push" — so what, exactly, is oscillating?
Key idea. An electromagnetic (EM) wave consists of oscillating electric and magnetic fields, at right angles to each other and to the direction the wave travels. No physical medium is required — an EM wave is a self-sustaining disturbance in the electric and magnetic fields themselves, and can travel through a vacuum (also called free space).
Key fact. The speed of light is actually derived purely from two universal constants and therefore, in the absence of a medium, will always have the same value. That means that all electromagnetic waves travel at the same speed in a vacuum, the speed of light: c = 3.00 × 10⁸ m s⁻¹. This is a universal constant — it does not depend on frequency or wavelength, or on the source.
Visible light is only a tiny slice of a much larger family. The full range of electromagnetic waves, ordered by wavelength (or equivalently by frequency, since v = ƒλ = c is fixed), is called the electromagnetic spectrum.
Fig. 6.2 The electromagnetic spectrum. The boundaries between regions are not sharp — this is a continuous spectrum, and the labels are just a convenient guide.
Important: when a light wave passes into a different transparent medium (e.g. from air into glass), its speed changes and so its wavelength changes (λ = v/ƒ) — but its frequency stays the same, because frequency is set by the source that originally produced the wave, not by the medium it happens to be passing through.
Worked example 6.1
A Wi-Fi router transmits at a frequency of 2.40 GHz. Calculate the wavelength of this signal in air (assume the speed of the signal in air ≈ c).
17A gamma ray has a wavelength of 2.0 × 10⁻¹³ m. Calculate its frequency in a vacuum.
ƒ = c/λ = (3.00×10⁸)/(2.0×10⁻¹³) = 1.5×10²¹ Hz.
18Identify which region of the electromagnetic spectrum is used by (a) a household microwave oven, (b) a television remote control, (c) an airport security body scanner.
a) microwaves; b) infrared; c) X-rays (millimetre-wave body scanners use microwaves — either is acceptable if justified).
19Explain why radio signals from a distant space probe can reach Earth, while a shout from an astronaut on that probe could not.
Radio waves are electromagnetic waves — oscillating electric and magnetic fields that require no medium and can cross the vacuum of space. A shout is a sound wave, which is mechanical and needs particles of a medium to compress and carry the disturbance; there is no such medium in space, so sound cannot travel between the probe and Earth.
7. Mechanical waves vs. electromagnetic waves
Sections 5 and 6 looked at sound and light individually. It's worth stepping back and comparing the two wave families directly, side by side.
Property
Mechanical waves
Electromagnetic waves
What oscillates?
particles of a physical medium
electric & magnetic fields
Needs a medium?
yes
no
Can cross a vacuum?
no
yes
Can be transverse or longitudinal?
yes — either, depending on the medium and wave type
always transverse
Speed depends on…
the properties of the medium (density, stiffness, temperature, …)
the medium too — but equals a fixed value c in a vacuum
Typical examples
sound, water waves, waves on strings, seismic waves
What they have in common. Despite these differences, both families are still described by the same underlying wave model — the same v = ƒλ = λ/T relationship applies to both, and (as the companion workbooks in this set explore) both mechanical and electromagnetic waves show reflection, refraction, diffraction and interference. The physical "carrier" is different, but the mathematics of wave behaviour is shared.
Check your understanding
20Classify each of the following as a mechanical wave or an electromagnetic wave: (a) an ocean swell, (b) a Wi-Fi signal, (c) the vibration felt from a passing truck, (d) sunlight, (e) an ultrasound scan.
a) mechanical (water wave); b) electromagnetic (radio/microwave); c) mechanical (a seismic/vibration wave through the ground); d) electromagnetic (light); e) mechanical (ultrasound is a high-frequency sound wave).
21A student claims: "Electromagnetic waves are just a special, very fast kind of mechanical wave." Explain what is scientifically wrong with this statement.
This is incorrect because the two are fundamentally different in what is oscillating and whether a medium is required. A mechanical wave is an oscillation of matter (particles of a medium) and cannot exist without that medium. An electromagnetic wave is an oscillation of electric and magnetic fields and requires no medium at all — it isn't simply a "fast" version of a mechanical wave, it is a different physical phenomenon that happens to obey the same general wave equations.
8. Wavefronts and rays
So far, every diagram in this workbook has shown a wave travelling in one dimension, along a single line. Real waves — ripples on a pond, sound spreading through a room, light leaving a bulb — spread out in two or three dimensions. To describe this, physicists use two complementary pictures: wavefronts and rays.
Key definitions.
Wavefront — a line (in 2D) or surface (in 3D) joining all the neighbouring points of a wave that are oscillating in phase with each other (for example, joining all the crests). Successive wavefronts are one wavelength apart.
Ray — a line showing the direction in which a wave is transferring energy. Rays are always perpendicular to the wavefronts at every point.
Fig. 8.1 A point source (e.g. a pebble dropped in a pond, or a lamp close up) produces circular/spherical wavefronts and radial rays. A source that is very far away compared to the wavelength (e.g. sunlight reaching Earth) produces wavefronts that are essentially flat and parallel — a "plane wave" — with parallel rays.
Live simulation: point source vs. distant source
Wavefronts & rays
New wavefronts (blue) continuously appear and spread outward, one wavelength apart; the rays (amber) always stay perpendicular to them.
Fig. 8.2 Toggle between a nearby point source and a very distant source to see the wavefronts flatten out.
Check your understanding
22Explain why sunlight reaching the Earth's surface is normally modelled using parallel rays, even though the Sun is technically a point source of spherical wavefronts.
The Sun is so far from the Earth (about 150 million km) compared to the size of the region being illuminated that the spherical wavefronts arriving are, for all practical purposes, flat over that region — a tiny patch of a huge sphere looks like a plane. So the wavefronts can be treated as parallel, and the rays (perpendicular to them) as parallel too.
23In a ripple tank, a dipper produces circular wavefronts spaced 2.0 cm apart, and the tank shows the wave travelling at 8.0 cm s⁻¹. Calculate the frequency at which the dipper is oscillating.
ƒ = v/λ = 8.0/2.0 = 4.0 Hz.
24State the geometric relationship between a ray and the wavefront it crosses, at the point where they cross.
They are always perpendicular (at right angles) to each other.
9. Reflection at boundaries
When a wave reaches a boundary between two different media, at least some of its energy is sent back into the medium it came from. This is reflection, and — remarkably — it obeys exactly the same rule for every kind of wave: water ripples off the side of a bath, sound off a canyon wall, or light off a mirror.
The law of reflection. The angle of incidence equals the angle of reflection, where both angles are measured from the normal — an imaginary line perpendicular to the surface at the point where the wave strikes it (not from the surface itself).
Fig. 9.1 Reflection of a single ray: the angle of incidence θᵢ (between the incident ray and the normal) equals the angle of reflection θᵣ (between the reflected ray and the normal).
Live simulation: check the law of reflection
Angle of incidence vs. reflection
Angle of incidence: …
Angle of reflection: … The reflected ray always mirrors the incident ray exactly.
Fig. 9.2 Drag the slider to change the incident ray's angle and confirm that the reflected ray always leaves at the same angle to the normal.
This law applies just as well to whole wavefronts, not just single rays: parallel wavefronts meeting a flat boundary reflect so that the angle the incoming wavefronts make with the boundary equals the angle the outgoing wavefronts make with it.
Fig. 9.3 Reflection of parallel wavefronts — the same geometry as Fig. 9.1, but drawn as the wavefronts (perpendicular to the rays) rather than the rays themselves. Each wavefront reflects at the exact point where it meets the surface (here, point P), and its spacing — the wavelength — is preserved on the way out.
The image the reflected rays appear to come from a plane mirror is as far behind the mirror as the real object is in front of it — this is why your reflection appears to be "inside" the mirror, the same distance away as you are.
Specular vs. diffuse reflection. Smooth, shiny, usually pale surfaces (glass, polished metal, still water) reflect parallel rays in an orderly, parallel way — specular reflection — which produces a clear image. Rough, matt, usually dark surfaces (fabric, unpolished stone, paper) reflect the same parallel rays off in many different directions — diffuse reflection, or scattering — which produces no clear image, even though each individual ray still obeys the law of reflection at the microscopic level.
Try it
A detector is placed inside a "mirror maze" made from several flat mirrors at right angles. A beam enters and reflects off three mirrors before reaching the detector, striking them at 45°, 60° and 30° respectively. Because the law of reflection applies at every surface independently, you can trace the beam's path through the whole maze one bounce at a time, just by applying θᵢ = θᵣ at each mirror in turn.
Check your understanding
25A light ray strikes a plane mirror at an angle of 35° to the mirror's surface (not to the normal). Calculate the angle of incidence and the angle of reflection, both measured from the normal.
Angle of incidence = 90° − 35° = 55° (measured from the normal, not the surface). By the law of reflection, angle of reflection = 55° also.
26State, with a reason, whether a sheet of white paper and a sheet of polished metal each produce a clear image by reflection.
Polished metal: yes, it produces a clear image, because its surface is smooth so parallel incoming rays are reflected in an orderly, still-parallel way (specular reflection). White paper: no, it does not produce a clear image, because its surface is rough at a microscopic level, so parallel incoming rays are scattered off in many different directions (diffuse reflection) even though each ray individually still obeys the law of reflection.
27Using the simulation above, set the angle of incidence to 65°. Predict the angle of reflection before checking the readout, then explain in one sentence why this relationship holds true for any type of wave, not just light.
The angle of reflection should also be 65°. The law of reflection is a general geometric consequence of how any wavefront reflects off a boundary — it doesn't depend on what the wave physically is (light, sound, water), only on the geometry of the boundary, so it applies equally to every kind of wave.
Glossary
Wave (travelling / progressive)
An oscillating disturbance that transfers energy away from a source, without net transfer of matter.
Propagation
The movement of a wave, and the energy it carries, away from its source.
Medium
The substance through which a mechanical wave travels.
Mechanical wave
A wave involving the oscillation of particles of a physical medium; cannot travel through a vacuum.
Electromagnetic wave
A transverse wave of oscillating, perpendicular electric and magnetic fields; requires no medium and travels at c = 3.00 × 10⁸ m s⁻¹ in a vacuum.
Transverse wave
A wave in which particle oscillation is perpendicular to the direction of energy transfer.
Crest / trough
The highest / lowest point of a transverse wave.
Longitudinal wave
A wave in which particle oscillation is parallel to the direction of energy transfer.
Compression / rarefaction
A region of increased / decreased particle density and pressure in a longitudinal wave.
Wavelength, λ
The shortest distance between two points on a wave oscillating in phase; e.g. crest to crest.
Amplitude
The maximum displacement of a particle from its equilibrium position.
Time period, T
The time taken for one complete oscillation, or for one wavelength to pass a fixed point.
Frequency, ƒ
The number of complete oscillations per second; ƒ = 1/T. Unit: hertz (Hz).
Wave speed, v
The speed at which a wave's energy is transferred; v = ƒλ = λ/T.
Pulse
A single, short-duration wave disturbance rather than a continuous repeating wave.
Sound
A longitudinal mechanical wave detectable by the human ear, typically 20 Hz – 20 kHz.
Ultrasound / infrasound
Sound frequencies above / below the human audible range.
Pitch / loudness
The perceived quality of sound corresponding to frequency / amplitude.
Vacuum (free space)
A region with no matter; electromagnetic waves can cross it, mechanical waves cannot.
Electromagnetic spectrum
The full continuous range of electromagnetic waves, from radio waves (long λ) to gamma rays (short λ).
Wavefront
A line or surface joining neighbouring points of a wave that are oscillating in phase; successive wavefronts are one wavelength apart.
Ray
A line showing the direction in which a wave transfers energy; always perpendicular to the wavefronts.
Plane wave
A wave with flat, parallel wavefronts, typically produced by a very distant source.
Reflection
The return of some or all of a wave's energy into its original medium when it meets a boundary.
Normal
An imaginary line perpendicular to a surface at the point where a ray meets it.
Angle of incidence / reflection
The angle between the incident / reflected ray and the normal.
Law of reflection
The angle of incidence equals the angle of reflection.