Wave Calculations
Year 10 (IGCSE) 🌊 Waves & Optics Solve problems using v = fλ; understand diffraction and interference.
🌊 v = fλ: Advanced Problem Solving
The wave equation links three key wave quantities. You must be comfortable rearranging and using it in complex situations.
🌊 Wave Equation
$$v = f\lambda \qquad f = \frac{v}{\lambda} \qquad \lambda = \frac{v}{f} \qquad T = \frac{1}{f}$$📡 Radio wave example: BBC Radio 1 broadcasts at 98.8 MHz. Speed = 3×10⁸ m/s.
λ = v/f = 3×10⁸ ÷ 98.8×10⁶ = 3.03 m
λ = v/f = 3×10⁸ ÷ 98.8×10⁶ = 3.03 m
🔊 Sound example: A sound wave in air (340 m/s) has wavelength 0.85 m. Find frequency.
f = v/λ = 340 ÷ 0.85 = 400 Hz
f = v/λ = 340 ÷ 0.85 = 400 Hz
🌊 Water waves: Period T = 4 s. Speed = 6 m/s. Find wavelength.
f = 1/T = 0.25 Hz. λ = v/f = 6/0.25 = 24 m
f = 1/T = 0.25 Hz. λ = v/f = 6/0.25 = 24 m
🔊 Diffraction
Diffraction is the spreading of waves when they pass through a gap or around an obstacle. It is most noticeable when the gap size ≈ the wavelength.
📻 Radio waves diffract around hills: Long wavelength (~1 km) radio waves diffract around hills and buildings easily — that's why you can receive AM radio in valleys!
💡 Light through a narrow slit: Visible light (wavelength ~500 nm) diffracts through tiny slits, creating bright and dark bands — a diffraction pattern.
Mobile phone signals (GHz frequencies, short λ) struggle to diffract around buildings — that's why you get dead spots in cities!
⚡ Wave Interference
When two waves meet, they superpose (add together). This creates constructive or destructive interference.
| 🌊 Type | 📝 Condition | 📊 Result |
|---|---|---|
| ✅ Constructive | Waves in phase (peaks align) | Amplitude doubles — louder/brighter |
| ❌ Destructive | Waves out of phase (peak meets trough) | Amplitude cancels — quieter/darker |
Noise-cancelling headphones use destructive interference — they create a sound wave that is the exact opposite (inverted) of the noise around you, cancelling it out!
Ready to test yourself? Click the Quiz tab above to answer questions on this topic!
🌊 Wave Calculations (v, f, λ, T)