💡 How to use this guide: Click any topic in the sidebar or above. Each section has simple explanations, key definitions to learn word-for-word, formulas with worked examples, and a quiz at the end. Work through them in order!
Chapter 1 — Waves
🌊 What is a Wave?
Waves are how energy travels without the medium itself travelling. Everything from sound to light to earthquakes is a wave!
📖 Definition — Wave
A wave is a means of transferring energy by oscillations from one place to another.
Two Types of Wave
Transverse Wave
⊥ perpendicular
Oscillation is PERPENDICULAR (at right angles) to the direction the wave travels.
Examples: Light, radio waves, waves on a rope, water waves.
Longitudinal Wave
∥ parallel
Oscillation is PARALLEL (same direction) to the direction the wave travels.
Examples: Sound waves in solids/liquids/gases, compression waves on a spring.
🧠 Easy memory trick: Think of a jump rope — you shake it UP and DOWN but the wave travels LEFT to RIGHT. That's transverse (the vibration crosses the direction of travel). Sound is different — the air compresses and expands IN THE SAME DIRECTION the sound travels. That's longitudinal.
Key Terms for Waves
📖 Wavelength (λ)
The wavelength (λ, "lambda") is the distance from one point on a wave to the corresponding point on the next cycle. Unit: metre (m).
📖 Frequency (f)
The frequency of a wave is the number of complete oscillations (full cycles) per second. Unit: hertz (Hz).
📖 Periodic Time (T)
The periodic time is the time it takes to complete one full cycle. T = 1/f. Unit: second (s).
📖 Amplitude
The amplitude of a wave is the maximum displacement from the rest position (the height of the wave). Amplitude determines the energy/loudness of the wave.
Chapter 1 — Waves
📏 Wave Equations (c = fλ)
The most important wave equation connects speed, frequency and wavelength. Master this and you can solve almost every wave maths question!
⚠️ The Main Wave Equation
c = fλ (or v = fλ)
c = wave speed (m s⁻¹) — also written as v f = frequency (Hz) λ = wavelength (m)
Relationship Between Period and Frequency
T = 1/f f = 1/T
T = periodic time (s) f = frequency (Hz)
If 5 waves pass per second (f=5Hz), each wave takes 1/5 = 0.2s to pass (T=0.2s)
🧠 Key speeds to remember:
Speed of light = 3 × 10⁸ m s⁻¹ (ALL electromagnetic waves in a vacuum)
Speed of sound in air ≈ 340 m s⁻¹
Quick Rearrangements
From c = fλ, you can rearrange to find any variable:
Find speed
c = fλ
Find frequency
f = c/λ
Find wavelength
λ = c/f
⚠️ Important: When a wave travels from one medium to another (e.g. light entering glass), its speed changes and wavelength changes, but its frequency stays the same!
Chapter 1 — Waves
✨ Properties of Waves
All waves — light, sound, water — share four key behaviours. These are your evidence that something is a wave!
📖 Reflection
Reflection is the bouncing of waves off an obstacle in their path. Examples: echoes (sound), mirrors (light).
📖 Refraction
Refraction is the changing of direction of a wave as it travels from one medium to another (due to a change in speed). Note: frequency does NOT change on refraction.
📖 Diffraction
Diffraction is the spreading of waves around a slit or an obstacle. It is only significant when the slit width is approximately equal to the wavelength.
📖 Interference
Interference occurs when waves from two sources meet to produce a wave of different amplitude.
🧠 Why can sound go around corners but light can't? Diffraction only works well when the gap is roughly the same size as the wavelength. Sound wavelengths are 1–10m (similar to doorway widths!) so sound diffracts around corners easily. Light wavelengths are ~500nm — much too small compared to a doorway, so light doesn't diffract through it.
🔬 Refractive Index
Refractive Index Formula
n = sin i / sin r
n = refractive index (no units) i = angle of incidence (measured from the normal) r = angle of refraction (measured from the normal)
Also: n = c/v (speed in medium 1 / speed in medium 2)
🧠 Refractive index in plain English: It tells you how much a material slows down light compared to a vacuum. Glass has n ≈ 1.5, meaning light travels 1.5 times slower in glass than in a vacuum.
Chapter 1 — Waves
🎭 Constructive & Destructive Interference
When two waves meet, they can add together or cancel each other out. This is the key evidence that light and sound are waves!
📖 Coherent Sources
Two waves are coherent if they have the same frequency and are in phase (or have a constant phase difference between them).
📖 Constructive Interference
Constructive interference occurs when waves from two coherent sources meet to produce a wave of GREATER amplitude. (Crest meets crest = bigger wave!)
📖 Destructive Interference
Destructive interference occurs when waves from two coherent sources meet to produce a wave of LOWER amplitude. (Crest meets trough = cancellation!)
🧠 Analogy: Imagine two people pushing a swing. If they both push at the same time (in phase) the swing goes higher — constructive. If one pushes while the other pulls (out of phase by half a wavelength), the swing barely moves — destructive!
🔊 Demonstrating Sound Interference
Connect two speakers to the same signal generator (same frequency!). Walk slowly in a line in front of the speakers. You'll hear the sound get louder and quieter alternately — this is constructive and destructive interference alternating as you change your distance from each speaker.
🎯 Exam key point: You MUST mention that both speakers are connected to the SAME signal generator (same frequency) to make coherent sources. Without this, you get no marks for the experiment!
💡 Young's Double Slit (Light)
Thomas Young proved light is a wave by shining it through two tiny slits and producing alternating bright and dark lines (fringes) on a screen. Bright lines = constructive interference. Dark lines = destructive interference. The fact that light interferes PROVES it is a wave!
Chapter 1 — Waves
📍 Stationary (Standing) Waves
When two waves of the same frequency travel in opposite directions, they create a stationary wave pattern — the basis of all musical instruments!
📖 Stationary (Standing) Wave
Stationary (or standing) waves are formed when two periodic waves of the same frequency and amplitude travelling in opposite directions meet.
Nodes and Antinodes
Node (N)
No movement
Points where the amplitude is always ZERO — destructive interference. The string doesn't move here at all.
Antinode (A)
Max movement
Points of maximum amplitude — constructive interference. The string vibrates most violently here.
📏 Key Relationships
Internodal Distance (distance between consecutive nodes)
Distance between 2 nodes = λ/2
The distance between two consecutive nodes = half a wavelength.
The distance between two consecutive antinodes = half a wavelength.
So if you know the length between nodes, you can find λ (just double it!), then use c=fλ.
🎵 Harmonics
A string can vibrate at different frequencies called harmonics. The simplest pattern (one antinode in the middle, nodes at both ends) is the fundamental frequency (1st harmonic). The string vibrates at 2× the fundamental = 2nd harmonic, and so on.
🎸 Guitar example: When you pluck a guitar string, it vibrates as a standing wave. The two ends are fixed = nodes. The middle vibrates = antinode. The length of the string = λ/2. So λ = 2L, and f = c/(2L).
Chapter 1 — Waves
🚑 The Doppler Effect
Ever noticed how an ambulance sounds higher-pitched as it approaches and lower-pitched as it drives away? That's the Doppler Effect!
📖 The Doppler Effect
The Doppler effect is the apparent change in the frequency of a wave due to the relative motion between the source of the wave and the observer.
🧠 Why Does it Happen?
Imagine a fire engine moving to the right, emitting sound waves. In front of the fire engine, the waves get compressed — they're closer together — so the wavelength is shorter and the frequency is higher (higher pitch). Behind the fire engine, the waves are stretched out — lower frequency (lower pitch).
f' = apparent (observed) frequency (Hz) f = actual frequency of the source (Hz) c = speed of the wave (m s⁻¹) u = speed of the moving source (m s⁻¹)
MITS rule — "Minus Is Towards":
Use MINUS (−) below the line when source is moving TOWARDS observer → higher f'
Use PLUS (+) below the line when source is moving AWAY → lower f'
🚑 MITS = Minus Is Towards: The minus sign gives a smaller bottom number → bigger answer → higher frequency. The plus sign gives a bigger bottom → smaller answer → lower frequency. Always ask yourself: is the source coming towards me or going away?
Applications of the Doppler Effect
Police speed traps: Radar guns bounce radio waves off cars and measure the frequency shift
Foetal monitoring: Ultrasound measures blood movement or foetal heartbeat
Weather forecasting: Doppler radar detects wind speed in clouds
Astronomy: Red shift — distant galaxies moving away → their light is shifted to longer (red) wavelengths (Edwin Hubble used this to prove the universe is expanding!)
⚠️ Common mistake: A racing car going past is an EXAMPLE of the Doppler effect — but NOT an application. Applications are things like speed traps and medical ultrasound.
Chapter 1 — Worked Examples
📐 Wave Calculations
Worked examples from the exam — c=fλ, stationary waves and the Doppler effect.
🧮 Example 1 — Basic Wave Speed
Q: A wave has frequency 5 Hz and wavelength 200 m. Calculate its speed.
Use c = fλ
c = f × λ = 5 × 200 = 1000 m s⁻¹
✅ Speed = 1000 m s⁻¹
🧮 Example 2 — Finding Wavelength from Speed and Frequency
Q: Orange light has frequency 5×10¹⁴ Hz. Speed of light = 3×10⁸ m s⁻¹. Find the wavelength.
Rearrange c = fλ to get λ = c/f
λ = c/f = (3×10⁸) / (5×10¹⁴) = 6×10⁻⁷ m = 600 nm
✅ Wavelength = 6×10⁻⁷ m (600 nm — this is in the orange part of the visible spectrum!)
🧮 Example 3 — Stationary Wave: Finding Frequency
Q: A violin string (length 328 mm) vibrates at its fundamental frequency. Speed of sound in string = 433 m s⁻¹. Find the frequency.
At fundamental frequency: distance between nodes = λ/2 = string length
λ/2 = 0.328 m → λ = 0.656 m
Use c = fλ → f = c/λ
f = 433 / 0.656 = 660 Hz
✅ Frequency = 660 Hz
🧮 Example 4 — Doppler Effect: Finding Apparent Frequency
Q: A fire engine (speed 30 m s⁻¹) emits sound at 2300 Hz as it approaches. Speed of sound = 340 m s⁻¹. Find the apparent frequency.
✅ Apparent frequency = 2523 Hz (higher than actual — source is approaching!)
🧮 Example 5 — Doppler Effect: Finding Speed of Source
Q: An ambulance emits 750 Hz. Observer detects 820 Hz as it approaches. Speed of sound = 340 m s⁻¹. Find speed of ambulance.
820 = 750 × 340 / (340 − u)
820(340 − u) = 750 × 340 278800 − 820u = 255000 820u = 23800 u = 29 m s⁻¹
✅ Speed of ambulance = 29 m s⁻¹
Chapter 1 — Quiz
✅ Quiz: Waves
Test yourself on Waves!
Chapter 2 — Sound
🔊 Sound is a Wave
Sound is a longitudinal wave that needs a medium to travel. It can't travel through a vacuum!
🔬 Experiment: Sound Needs a Medium
Place an electric bell inside a bell jar. You can hear it ringing. Now use a vacuum pump to remove all the air from the bell jar. The bell can still be SEEN to ring, but the sound gets quieter and quieter until you hear nothing. This proves sound cannot travel through a vacuum — it needs a medium (matter) to travel through.
🎯 Conclusion: Sound is a mechanical wave — it needs particles to pass energy from one place to another. Light is an electromagnetic wave — it doesn't need a medium (which is why we can see stars in space but cannot hear them!).
🔊 How Does Sound Travel?
Sound travels by compressing and then stretching the air in front of it (compressions and rarefactions). Molecules vibrate back and forth in the same direction the sound travels — that's why sound is a longitudinal wave.
🧠 Why does sound travel faster in water than air? Water molecules are much closer together than air molecules. When one molecule vibrates, it bumps into its neighbour almost instantly. The energy travels faster when the molecules are packed closer together!
Chapter 2 — Sound
🎸 Resonance & Natural Frequency
Every object has a natural frequency. Hit it at that frequency and it vibrates like crazy — that's resonance!
📖 Natural Frequency
The natural frequency of an object is the frequency at which the object will vibrate if free to do so.
📖 Resonance
Resonance is the transfer of energy so that a body vibrates at its natural frequency.
🧠 Opera singer shattering glass: The singer sings at exactly the natural frequency of the glass. Energy is transferred by resonance. The glass vibrates more and more violently until it shatters! This is also why soldiers break step when marching across a bridge (they don't want to set up resonance and collapse it).
🎸 Factors Affecting Frequency of a Stretched String
Factor
Relationship
Meaning
Length (L)
f ∝ 1/L
Longer string → lower frequency (like a bass guitar vs guitar)
Tension (T)
f ∝ √T
Higher tension → higher frequency (tune up by tightening)
Mass per unit length (μ)
f ∝ 1/√μ
Thicker/heavier string → lower frequency
⚠️ Frequency of a Stretched String (HL)
f = (1/2L)√(T/μ)
f = fundamental frequency (Hz) L = length (m) T = tension (N) μ = mass per unit length (kg m⁻¹)
🎯 Tension exam shortcut: If tension increases by factor 9, frequency increases by √9 = 3. If tension doubles, frequency increases by √2 ≈ 1.41. Always take the square root of the tension factor!
🎻 Demonstrating Resonance
Use two IDENTICAL tuning forks on a soundboard. Set one vibrating and place it on the board. Then stop it. The second fork will now be heard vibrating — resonance transferred energy between them because they have the SAME natural frequency.
🎯 Key point: Both tuning forks must have the SAME frequency. This is essential to mention in the exam!
Chapter 2 — Sound
📣 Sound Intensity & Decibels
How loud is a sound? Sound intensity is the power per unit area reaching your ear. Decibels are how we measure loudness in practice.
📖 Sound Intensity
Sound intensity is defined as power per unit area. Unit: W m⁻².
⚠️ Sound Intensity Formula
I = P / (4πr²)
I = sound intensity (W m⁻²) P = power of sound source (W) r = distance from source (m)
4πr² = surface area of a sphere (sound spreads out in all directions)
🧠 Inverse square law: Sound intensity ∝ 1/r². If you double your distance from a speaker, the sound intensity becomes 4× smaller (gets 4 times quieter). Move 3× further away → 9× quieter!
🔉 The Decibel Scale
📖 Threshold of Hearing
The threshold of hearing is the smallest sound intensity detectable by the average human ear at a frequency of 1000 Hz. Its value is 1×10⁻¹² W m⁻².
Whisper
20 dB
Conversation
60 dB
Rock concert
110 dB
Threshold of pain
130 dB
🔑 Key Decibel Rule
Doubling Sound Intensity Rule
Double the intensity → +3 dB
If sound intensity DOUBLES, sound intensity LEVEL increases by 3 dB.
Intensity ×4 → +6 dB (doubled twice: 3+3)
Intensity ×8 → +9 dB (doubled three times: 3+3+3)
Reverse: +9 dB means intensity increased by factor of 8 (= 2×2×2)
🎚️ The dB(A) Scale
The human ear is most sensitive to frequencies between 2000 Hz and 4000 Hz. The dB(A) scale adjusts readings to match the ear's frequency response — it's a weighted scale that reflects what we actually hear as loud.
📖 Frequency Limits of Audibility
The frequency limits of audibility are the highest and lowest frequencies that can be heard by a normal human ear: 20 Hz – 20,000 Hz.
Chapter 2 — Sound
🎵 Harmonics & Sound in Pipes
Musical instruments work because of standing waves in strings and pipes. Understanding this explains why flutes and clarinets sound different!
📖 Harmonics
Frequencies which are integer multiples of the fundamental frequency f are called harmonics. The fundamental is the 1st harmonic, 2f is the 2nd harmonic, 3f is the 3rd harmonic, etc.
Pipes Open at Both Ends (Open Pipes)
An open pipe always has an antinode at both ends. The fundamental frequency has λ/2 fitting in the pipe length (L = λ/2). So λ = 2L, and f = c/(2L).
🎺 Open pipe harmonics: All harmonics present (1f, 2f, 3f, 4f ...). Examples: flute, trumpet, open organ pipe.
Pipes Open at One End (Closed Pipes)
A closed pipe always has a node at the closed end and an antinode at the open end. The fundamental has λ/4 fitting in the pipe length (L = λ/4). So λ = 4L, and f = c/(4L).
🎵 Closed pipe harmonics: Only ODD harmonics present (1f, 3f, 5f ...). Examples: clarinet, closed organ pipe. This is why clarinets sound more "hollow" than flutes!
Pipe Type
Ends
Fundamental
Harmonics
Open at both ends
Antinode-Antinode
L = λ/2
All: 1f, 2f, 3f...
Closed at one end
Node-Antinode
L = λ/4
Odd only: 1f, 3f, 5f...
🎯 Exam tip on drawing harmonics: Always put nodes at closed ends and antinodes at open ends. For the 3rd harmonic of a closed pipe: node at closed end, then antinode, node, antinode — that's 3 quarter-wavelengths total in the pipe length.
Chapter 2 — Sound
🧪 Experiment: Measuring Speed of Sound
A key mandatory experiment — you need to know the apparatus, procedure, formula and precautions!
Apparatus
Graduated cylinder, resonance tube (open at both ends), tuning forks of known frequency, metre stick, digital callipers.
Procedure (the key steps)
Strike the tuning fork and hold it over the resonance tube
Move the inner tube slowly UP until you hear the first loud resonant sound
Measure the length l from top of tube to water surface
Measure the inner diameter d of the tube using digital callipers
Note the frequency from the tuning fork
Repeat with different tuning forks and calculate average speed
⚠️ Formula for Speed of Sound
c = 4f(l + 0.3d)
c = speed of sound (m s⁻¹) f = frequency of tuning fork (Hz) l = length of air column at resonance (m) d = diameter of tube (m) — the end correction (0.3d) accounts for the fact that the antinode forms slightly above the top of the tube
Precautions
Keep your eye level with the tube top when measuring l (avoid parallax error)
Start with the inner tube fully in the water and raise slowly (to find the FIRST harmonic, not a higher one)
Repeat several times for each fork and take the average
You must measure the diameter because of the end correction — the sound antinode forms slightly outside the tube, not exactly at the top
🎯 Alternative method (no need to measure diameter): Find both the 1st AND 2nd position of resonance for the same tuning fork. Distance between them = λ/2. So λ = 2(L₂ − L₁), then c = fλ. The end correction cancels out!
Chapter 2 — Sound
🎼 Characteristics of Musical Notes
Three properties distinguish musical notes from each other — and they're all linked to wave properties!
Property
Depends on
Example
Loudness
Amplitude of the sound wave
Hitting a drum hard → larger amplitude → louder sound
Pitch
Frequency of the sound wave
High frequency → high pitched (squeaky) sound
Quality (Timbre)
Number and relative strength of overtones (harmonics)
Middle C sounds different on piano vs violin because of different overtones present
🎸 Quality explained: Almost no real instrument plays a pure single frequency. A guitar string vibrates at its fundamental frequency PLUS many overtones simultaneously. The unique blend of these overtones gives each instrument its distinctive sound (quality/timbre).
Chapter 2 — Worked Examples
📐 Sound Calculations
Sound intensity, frequency of strings, resonant pipes — all worked step by step.
🧮 Example 1 — Sound Intensity
Q: A loudspeaker has power 20 mW. Calculate sound intensity 6 m away.
I = P / (4πr²)
I = (20×10⁻³) / (4π × 6²) I = 0.02 / (4π × 36) I = 0.02 / 452.4 I = 4.4×10⁻⁵ W m⁻²
✅ Sound intensity = 4.4×10⁻⁵ W m⁻²
🧮 Example 2 — Decibel Change
Q: Sound intensity level increases from 85 dB to 94 dB at a concert. By what factor has sound intensity increased?
Increase = 94 − 85 = 9 dB. Each 3 dB = doubling
9 dB = 3 dB + 3 dB + 3 dB = 3 doublings Factor = 2 × 2 × 2 = 8
✅ Sound intensity increased by a factor of 8
🧮 Example 3 — Frequency of a String (Tension Changes)
Q: A string vibrates at 205 Hz when tension is 5 N. Find frequency when tension increases to 10 N.
f ∝ √T. Tension ratio = 10/5 = 2
New frequency = √2 × 205 = 1.414 × 205 = 290 Hz
✅ New frequency = 290 Hz
🧮 Example 4 — Closed Pipe: Fundamental Frequency
Q: The ear canal is a closed pipe of length 2.3 cm. Speed of sound = 340 m s⁻¹. Find the fundamental frequency.
Closed pipe fundamental: L = λ/4, so λ = 4L
λ = 4 × 0.023 = 0.092 m
f = c/λ
f = 340 / 0.092 = 3696 Hz
✅ Fundamental frequency = 3696 Hz (This is why our ears are so sensitive to frequencies around 4000 Hz!)
Chapter 2 — Quiz
✅ Quiz: Sound
Test yourself on Sound!
Chapter 3 — Light
💡 Light as a Wave — Young's Double Slit
How do we know light is a wave? Because it INTERFERES! Thomas Young's brilliant experiment proved it in 1801.
Young's Double Slit Experiment
Young set up three screens. The first had one slit, the second had two slits close together, and the third was a viewing screen. Light from the single slit hits both slits of the second screen simultaneously — making them two coherent sources.
The light from both slits diffracts and overlaps. Where crests meet crests → bright bands (constructive interference). Where crests meet troughs → dark bands (destructive interference). The result is alternating bright and dark fringes on the screen.
📖 Conclusion of Young's Experiment
The fact that light undergoes interference tells us that light travels as a wave.
🧠 Why monochromatic light? "Monochromatic" means single wavelength (one colour). If you use white light (many wavelengths), each wavelength interferes at different positions and you get coloured fringes instead of clear bright/dark lines.
🔬 Modern Version: Laser + Diffraction Grating
Instead of Young's two slits, we now use a laser (monochromatic, coherent light) and a diffraction grating (hundreds of slits). This produces a much clearer, brighter interference pattern and lets us measure the wavelength of light precisely.
Chapter 3 — Light
🔬 The Diffraction Grating (nλ = d sinθ)
A diffraction grating has thousands of slits per millimetre. It splits light into precise colours, allowing us to measure the exact wavelength of light!
📖 Diffraction Grating
A diffraction grating consists of a piece of transparent material on which a very large number of opaque (black) parallel lines are engraved. The distance between adjacent slits is the grating constant d.
Finding the Grating Constant d
d = 1 / N (lines per metre)
If the grating has 600 lines/mm → 600,000 lines/m
d = 1 / 600,000 = 1.67×10⁻⁶ m
Remember: convert lines per mm to lines per METRE first (multiply by 1000)!
⚠️ Diffraction Grating Formula
nλ = d sinθ
n = order of image (1st order: n=1, 2nd order: n=2, etc.) λ = wavelength of light (m) d = grating constant (m) — distance between adjacent slits θ = angle between straight-through (n=0) position and the order in question
⚠️ CRITICAL exam warning: If the question gives you the distance between the nth order images (both sides), you MUST divide by 2 to get the distance to ONE side, then use tan θ = (x/2) / D to find θ. Many students forget this and lose marks!
Maximum Number of Images
Maximum Order Formula
n_max = d / λ
When θ = 90°, sinθ = 1, so nλ = d becomes n_max = d/λ
Round DOWN to the nearest whole number!
Total images = 2 × n_max + 1 (multiply by 2 for both sides, add 1 for centre)
Effect of Changing λ or d
Longer wavelength (λ↑)
sinθ = nλ/d → bigger sinθ → bigger θ → images spread further APART. Red light spreads more than blue!
White light is a mixture of all colours. Dispersion separates these colours because different wavelengths bend by different amounts.
📖 Dispersion
Dispersion is the separating out of the different colours present in white light. It occurs when white light passes through a prism or diffraction grating.
Why Does a Prism Cause Dispersion?
A prism disperses white light because the refractive index of glass is slightly different for different wavelengths. Violet light is refracted (bent) the most, red light the least. This is why "violet bends most violently"!
Why Does a Diffraction Grating Cause Dispersion?
From nλ = d sinθ: different wavelengths (λ) give different angles (θ). So different colours appear at different positions on the screen.
⚠️ Key difference: In a PRISM, red deviates least, violet deviates most. In a DIFFRACTION GRATING, red deviates most (longer wavelength → larger sinθ), violet deviates least. They're opposite!
🎨 Primary and Secondary Colours
Primary Colours of Light
🔴 🟢 🔵
Red, Green, Blue Mix all three equally → white light
Secondary Colours
Cyan · Magenta · Yellow
Red + Green = Yellow Red + Blue = Magenta Green + Blue = Cyan
Complementary Pairs
Blue & Yellow → White Green & Magenta → White Red & Cyan → White
🌈 Colours and Wavelength
Colour
Position in spectrum
Wavelength
Red
Longest wavelength, lowest frequency
~700 nm
Violet
Shortest wavelength, highest frequency
~400 nm
Remember: ROYGBIV — Red Orange Yellow Green Blue Indigo Violet (Richard Of York Gave Battle In Vain)
Chapter 3 — Light
📡 The Electromagnetic Spectrum
Visible light is just a tiny part of a huge family of electromagnetic waves. They all travel at the speed of light but have very different wavelengths and uses!
📖 The Electromagnetic Spectrum
The electromagnetic spectrum is the full range of electromagnetic radiation divided by frequency and wavelength. All EM waves travel at 3×10⁸ m s⁻¹ in a vacuum.
Radio
Micro
Infrared
Visible
UV
X-ray
Gamma
← Longer wavelength / Lower frequency Higher frequency / Shorter wavelength →
Radiation
Properties
Applications
Hazards
Infrared (IR)
EM wave, frequency less than visible light
Night-vision cameras, TV remotes, medical imaging (breast cancer detection)
Heating of tissue at high intensities
Ultraviolet (UV)
EM wave, frequency greater than visible light, causes fluorescence
High frequency EM, penetrate soft tissue but not bone/metal
Medical imaging (bones), airport security
Ionising — can cause cancer
Gamma rays
Highest frequency EM, from nuclear decay
Cancer treatment (radiotherapy), sterilising food
Highly ionising — causes cancer, cell death
🎯 Exam question: "Can you get a suntan through glass?"
Yes, but only weakly. Most UVB (which causes tanning/burning) is blocked by glass. However UVA (which makes up 95% of UV and can cause skin cancer without tanning) DOES penetrate glass. This is why you should wear sunscreen even on cloudy days!
Chapter 3 — Light
🔭 Polarisation
Only transverse waves can be polarised. The fact that light can be polarised is proof that light is a TRANSVERSE wave!
📖 Polarised Wave
A polarised wave is a wave which vibrates in one plane only.
🕶️ How Polarisation Works
Normal (unpolarised) light vibrates in all planes simultaneously. A polaroid filter only allows light vibrating in one specific plane to pass through — the output is polarised light.
Hold one polaroid up to light — it looks slightly dimmer but you can see through it
Pass the polarised light through a second polaroid: if both are aligned in the same direction, light passes
Rotate the second polaroid by 90° — NO light gets through at all! Completely dark!
📖 Key Conclusion from Polarisation
Only transverse waves can be polarised. The fact that light can be polarised proves that light is a transverse wave.
🕶️ Applications of Polarisation
Polaroid sunglasses: Sunlight reflecting off water/roads becomes horizontally polarised (causing glare). Sunglasses have vertically oriented polaroids that block this horizontal light → reduces glare
Stress polarisation: Engineers shine polarised light through plastic models of structures. Where there is stress, the polarisation changes and you can see the stress patterns as coloured regions
Chapter 3 — Light
🌌 Doppler Effect & Red Shift
The Doppler effect applies to light too — and it's how Edwin Hubble proved the universe is expanding!
🌌 Red Shift
When a star or galaxy moves AWAY from us, the light waves it emits get stretched out — the wavelength increases (shifts towards the red end of the spectrum). This is called red shift.
Edwin Hubble (1929) noticed that EVERY distant galaxy showed red shift — they were all moving away from us! This proved the universe is EXPANDING, which led to the Big Bang theory.
🔵 Blue shift: If a star is moving TOWARDS us, its wavelengths get compressed → shifts towards blue end of spectrum (blue shift). This is much rarer — only a few nearby galaxies show blue shift.
🧮 Calculating Speed from Red Shift
To find the speed of a moving star using the Doppler effect on light:
Use c = fλ to find the ACTUAL frequency from the known wavelength in a lab
Use c = f'λ' to find the APPARENT frequency from the observed (shifted) wavelength
Use the Doppler formula: f' = f × c / (c ± u) to find the speed u
🎯 Key point: If the wavelength INCREASED (red shift), the star is moving AWAY. Use the + sign in the Doppler formula denominator (c + u). If wavelength decreased (blue shift), star is approaching — use (c − u).
Chapter 3 — Worked Examples
📐 Light Calculations
Diffraction grating, wavelength of light, and red shift — all worked step by step.
🧮 Example 1 — Finding Grating Constant d
Q: A diffraction grating has 300 lines per mm. Find d.
Convert to lines per metre
300 lines/mm × 1000 = 300,000 lines/m
d = 1 / N
d = 1/300,000 = 3.33×10⁻⁶ m
✅ d = 3.33×10⁻⁶ m
🧮 Example 2 — Diffraction Grating: Finding Wavelength
Q: Grating has 80 lines/mm. Distance from grating to screen = 90 cm. Distance between 3rd order images = 23.8 cm. Find wavelength.
Find d: 80 lines/mm = 80,000 lines/m → d = 1/80,000 = 1.25×10⁻⁵ m
d = 1.25×10⁻⁵ m
Find θ: distance to ONE 3rd-order image = 23.8/2 = 11.9 cm = 0.119 m
tan θ = 0.119/0.90 → θ = tan⁻¹(0.119/0.9) = 7.53°
Use nλ = d sinθ with n=3
λ = d sinθ / n = (1.25×10⁻⁵)(sin 7.53°) / 3 λ = (1.25×10⁻⁵)(0.1309) / 3 = 5.46×10⁻⁷ m
✅ Wavelength = 5.46×10⁻⁷ m = 546 nm (green light!)
🧮 Example 3 — Maximum Number of Images
Q: Sodium light λ=589 nm, grating 300 lines/mm. Find the maximum order and total number of images.
d = 1/300,000 = 3.33×10⁻⁶ m
d = 3.33×10⁻⁶ m
n_max = d/λ
n_max = (3.33×10⁻⁶) / (589×10⁻⁹) = 5.65 → round down to 5
Total images = 2n_max + 1
Total = 2×5 + 1 = 11 images
✅ Maximum order = 5, Total images = 11
🧮 Example 4 — Red Shift: Speed of a Star
Q: Yellow helium line: lab wavelength = 587 nm, star wavelength = 590 nm. Is the star moving towards or away? Find its speed. (c = 3×10⁸ m s⁻¹)
Wavelength INCREASED → red shift → star is moving AWAY
Use + sign in Doppler formula (MITS: moving away = plus)
Find actual frequency: f = c/λ
f = 3×10⁸ / 587×10⁻⁹ = 5.111×10¹⁴ Hz
Find apparent frequency: f' = c/λ'
f' = 3×10⁸ / 590×10⁻⁹ = 5.085×10¹⁴ Hz
f'(c + u) = f×c → solve for u
u = [fc/f' − c] = c(f/f' − 1) u = 3×10⁸ × (5.111/5.085 − 1) = 3×10⁸ × 0.00511 ≈ 1.53×10⁶ m s⁻¹
✅ Star is moving AWAY at 1.53×10⁶ m s⁻¹ (1.5 million m/s!)
Chapter 3 — Quiz
✅ Quiz: Light
Test yourself on Light!
📋 All Formulas — Quick Reference
Every formula you need for the Leaving Cert Waves, Sound and Light exam. Learn these!
Chapter 1 — Waves
Wave Equation
c = fλ T = 1/f
c=speed (m s⁻¹), f=frequency (Hz), λ=wavelength (m), T=periodic time (s)
Refractive Index
n = sin i / sin r n = c/v
Stationary Waves
Distance between 2 nodes = λ/2
⚠️ Doppler Effect
f' = f × c / (c ∓ u)
MITS: Minus Is Towards. − when approaching, + when moving away
Chapter 2 — Sound
Sound Intensity
I = P / (4πr²)
Double I → +3 dB. ×4 → +6 dB. ×8 → +9 dB.
⚠️ Frequency of a Stretched String
f = (1/2L)√(T/μ)
L=length (m), T=tension (N), μ=mass per unit length (kg m⁻¹)
Speed of Sound Experiment
c = 4f(l + 0.3d)
l=length of air column, d=diameter of tube
Chapter 3 — Light
Grating Constant
d = 1/N (N = lines per metre)
⚠️ Diffraction Grating
nλ = d sinθ
n=order, λ=wavelength (m), d=grating constant (m), θ=angle from straight-through
Maximum Order
n_max = d/λ Total images = 2n_max + 1
Speed of light
3×10⁸ m s⁻¹
Speed of sound (air)
≈340 m s⁻¹
Threshold of hearing
10⁻¹² W m⁻²
Audible range
20–20,000 Hz
📖 All Definitions — Learn These Off!
These are the exact definitions you need for the exam. Learn them word for word!
Chapter 1 — Waves
Wave
A wave is a means of transferring energy by oscillations from one place to another.
Transverse Wave
A transverse wave is a wave where the direction of oscillation is perpendicular to the direction in which the wave travels.
Longitudinal Wave
A longitudinal wave is a wave where the direction of oscillation is parallel to the direction in which the wave travels.
Wavelength (λ)
The wavelength of a wave is the distance from one point on the wave to the corresponding point on the next cycle. Unit: metre (m).
Frequency (f)
The frequency of a wave is the number of complete oscillations per second. Unit: hertz (Hz).
Reflection
Reflection is the bouncing of waves off an obstacle in their path.
Refraction
Refraction is the changing of direction of a wave as it travels from one medium to another.
Diffraction
Diffraction is the spreading of waves around a slit or an obstacle. It is only significant when the slit width is approximately equal to the wavelength.
Interference
Interference occurs when waves from two sources meet to produce a wave of different amplitude.
Coherent Sources
Two waves are said to be coherent if they have the same frequency and are in phase (or have a constant phase difference).
Constructive Interference
Constructive interference occurs when waves from two coherent sources meet to produce a wave of greater amplitude.
Destructive Interference
Destructive interference occurs when waves from two coherent sources meet to produce a wave of lower amplitude.
Stationary (Standing) Wave
Stationary waves are formed when two periodic waves of the same frequency and amplitude travelling in opposite directions meet.
The Doppler Effect
The Doppler effect is the apparent change in the frequency of a wave due to the relative motion between the source of the wave and the observer.
Chapter 2 — Sound
Natural Frequency
The natural frequency of an object is the frequency at which the object will vibrate if free to do so.
Resonance
Resonance is the transfer of energy so that a body vibrates at its natural frequency.
Sound Intensity
Sound intensity is defined as power per unit area. Unit: W m⁻².
Threshold of Hearing
The threshold of hearing is the smallest sound intensity detectable by the average human ear at a frequency of 1000 Hz. Its value is 1×10⁻¹² W m⁻².
Frequency Limits of Audibility
The frequency limits of audibility are the highest and lowest frequencies that can be heard by a normal human ear: 20 Hz to 20,000 Hz.
Chapter 3 — Light
Diffraction Grating
A diffraction grating consists of a piece of transparent material on which a very large number of opaque parallel lines are engraved.
Dispersion
Dispersion is the separating out of the different colours present in white light.
Polarised Wave
A polarised wave is a wave which vibrates in one plane only.
Electromagnetic Spectrum
The electromagnetic spectrum is the full range of electromagnetic radiation divided by frequency and wavelength. All EM waves travel at 3×10⁸ m s⁻¹ in a vacuum.
🎯 Exam tip: Key words in definitions are worth marks. Words like "perpendicular", "parallel", "coherent", "per unit area", "natural frequency", "apparent change" are what the examiners look for. Don't leave them out!