Waves
Waves tests how energy and information travel without bulk matter moving with the wave. HKDSE questions cover wave properties, reflection, refraction, diffraction, interference, stationary waves, sound, and the electromagnetic spectrum; you are expected to connect a wave graph or experimental set-up to the wave equation and to path-difference reasoning.
Core rules and concepts
- A wave transfers energy and momentum. Transverse waves oscillate perpendicular to the direction of travel; longitudinal waves oscillate parallel to it.
- The wave equation is v = fλ. Frequency is set by the source; speed depends on the medium.
- Reflection, refraction, diffraction, and interference apply to all waves. Refraction occurs because speed changes at a boundary.
- For two coherent sources, constructive interference occurs when path difference is a whole number of wavelengths; destructive interference occurs at half-integer multiples.
- In a stationary wave, nodes have zero amplitude and antinodes have maximum amplitude; adjacent nodes are half a wavelength apart.
- Sound needs a medium; electromagnetic waves do not.
Worked example
In a double-slit experiment, slits are 0.50 mm apart, the screen is 2.0 m away, and adjacent bright fringes are 1.2 mm apart. Find the wavelength.
Use Δy = λD/a, so λ = Δy a / D. Convert to metres: Δy = 1.2 × 10⁻³ m, a = 0.50 × 10⁻³ m, D = 2.0 m. λ = (1.2 × 10⁻³)(0.50 × 10⁻³)/2.0 = 3.0 × 10⁻⁷ m = 300 nm. The fringe spacing is measured from the centre of one bright fringe to the next, not from a bright fringe to the nearest dark fringe.
Traps that cost marks
- Using the wrong distance in the double-slit formula; a is slit separation, D is slit-to-screen distance.
- Measuring fringe spacing as bright-to-dark instead of bright-to-bright.
- Assuming frequency changes when a wave enters a new medium; it is the speed and wavelength that change.
- Forgetting that path difference must be expressed in the same units as wavelength.
- Treating a stationary wave as a travelling wave; its nodes do not move along the medium.