Waves
This domain tests wave behaviour rather than circuit or material models: the wave equation, phase and path difference, superposition, stationary waves, sound, diffraction and the Doppler effect. You need to move confidently between frequency, wavelength, speed and phase.
Core rules
- v = fλ for all waves; for a stretched string v = √(T/μ).
- Two waves interfere constructively when path difference is nλ and destructively when it is (n + ½)λ, for coherent sources in phase.
- In a stationary wave, nodes are separated by λ/2; the distance between adjacent nodes and antinodes is λ/4.
- Diffraction is greatest when the gap is comparable to the wavelength. A diffraction grating maximum satisfies d sin θ = nλ.
- Doppler shift for sound: f′ = f(v ± vo)/(v ∓ vs), with signs chosen so approach raises frequency.
Worked example
In a Young’s double-slit experiment, λ = 589 nm, slit separation d = 0.50 mm and screen distance D = 1.5 m. Fringe spacing w = λD/d. Convert: λ = 5.89 × 10⁻⁷ m and d = 5.0 × 10⁻⁴ m. Then w = (5.89 × 10⁻⁷)(1.5)/(5.0 × 10⁻⁴) = 1.77 × 10⁻³ m, about 1.8 mm. The small-angle approximation is justified because w is much less than D.
Traps
- Entering nm or mm directly into a formula without converting to metres.
- Confusing path difference with phase difference; one wavelength equals 2π radians.
- Claiming a stationary wave transfers energy along the string; it does not.
- Using the double-slit spacing formula for a grating with many slits.
- Forgetting that sound needs a medium but light does not.