Contents
1. Wave Properties
| Term | Definition | Unit |
|---|---|---|
| Amplitude | Maximum displacement from equilibrium | m |
| Wavelength (λ) | Distance between two adjacent identical points (e.g. crest to crest) | m |
| Frequency (f) | Number of complete waves per second | Hz |
| Period (T) | Time for one complete wave: T = 1/f | s |
| Wave speed (v) | Distance travelled per second | m/s |
A wave has frequency 200 Hz and wavelength 1.5 m. Find its speed.
v = fλ = 200 × 1.5 = 300 m/s
Transverse vs longitudinal
| Transverse | Longitudinal |
|---|---|
| Vibration is perpendicular to direction of travel | Vibration is parallel to direction of travel |
| Has crests and troughs | Has compressions and rarefactions |
| Examples: light, water waves, all EM waves | Example: sound |
2. Reflection
Angle of incidence = angle of reflection (both measured from the normal — a line perpendicular to the surface at the point of incidence).
In a plane mirror, the image is: the same size as the object; the same distance behind the mirror as the object is in front; laterally inverted (left-right reversed); virtual (cannot be projected on a screen).
3. Refraction
Refraction is the change in direction of a wave when it crosses a boundary between two media of different densities, caused by a change in wave speed.
| Crossing boundary | Speed | Wavelength | Direction |
|---|---|---|---|
| Less dense → more dense (air → glass) | Decreases | Decreases | Bends towards normal |
| More dense → less dense (glass → air) | Increases | Increases | Bends away from normal |
When a wave refracts, its frequency stays the same. Only speed and wavelength change. Since v = fλ and f is constant, if v decreases, λ must also decrease.
4. Total Internal Reflection (TIR)
TIR occurs when light travels from a more dense medium to a less dense medium AND the angle of incidence exceeds the critical angle. At the critical angle, refracted ray travels along the boundary (90° to normal).
- Applications: optical fibres (internet/medical endoscopes), periscopes with prisms, diamonds.
- For glass, critical angle ≈ 42°. For water, critical angle ≈ 49°.
Both conditions must be met: (1) light must be going from denser to less dense medium, AND (2) angle of incidence must exceed the critical angle. If only one condition is met, TIR does not occur.
5. Electromagnetic Spectrum
All EM waves travel at the speed of light (3 × 10⁸ m/s) in a vacuum. They are transverse waves and require no medium.
| Wave type | Typical use | Hazard (if any) |
|---|---|---|
| Radio waves (longest λ) | Broadcasting, communications | None significant |
| Microwaves | Cooking, satellite communication | Internal heating of tissue |
| Infrared | Remote controls, thermal imaging | Skin burns |
| Visible light | Vision, photography | None at normal levels |
| Ultraviolet | Sterilisation, security marking | Skin cancer, eye damage |
| X-rays | Medical imaging | Cell damage, cancer risk |
| Gamma rays (shortest λ) | Cancer treatment, sterilising | Cell damage, cancer, death |
6. Sound Waves
Sound is a longitudinal wave — it requires a medium to travel and cannot travel through a vacuum. Speed of sound in air ≈ 340 m/s; in water ≈ 1500 m/s; in steel ≈ 5000 m/s.
- Higher frequency = higher pitch.
- Larger amplitude = louder sound.
- Human hearing range: 20 Hz to 20 000 Hz.
- Ultrasound (>20 000 Hz): used in medical imaging and sonar.
- v = f x lambda. Frequency does NOT change when wave passes between media - only speed and wavelength change.
- Transverse: vibration perpendicular to propagation. All EM waves, water waves.
- Longitudinal: vibration parallel to propagation. Sound waves. Cannot travel in vacuum.
- Refraction: light bends TOWARDS normal when slowing down (entering denser medium).
- Critical angle c: sin(c) = 1/n (n = refractive index). TIR occurs when angle > critical angle, denser to less dense medium.
- EM spectrum (increasing frequency): Radio, Microwave, IR, Visible, UV, X-ray, Gamma.
7. Common Exam Traps
All angles in reflection and refraction are measured from the normal, not from the surface. The normal is a line perpendicular to the surface at the point of contact.
Sound needs a medium. Light and all EM waves do not. "In space, no one can hear you scream" — but they can see the light from your torch.
Remember by increasing frequency (decreasing wavelength): Radio, Micro, Infrared, Visible, UV, X-ray, Gamma. A common mnemonic: "Raging Martians Invaded Venus Using X-ray Guns."
Key Terms — Flashcard Review
Tap each card to reveal the definition.
🎯 Practice Quiz — Test Yourself
8 O Level-style questions on this topic. Select an answer to see instant feedback.
Original study notes for Singapore students. Not affiliated with MOE, SEAB or Cambridge.