Waves (AS91170)
Waves (AS91170)
The waves standard tests wave behaviour, superposition, reflection and refraction, diffraction, standing waves and the Doppler effect. You need to link a physical situation to the correct wave model and use the wave equation accurately.
Core rules
- Wave speed v = fλ; period T = 1/f. Frequency is set by the source and does not change on refraction; speed and wavelength do.
- Transverse waves oscillate perpendicular to energy transfer; longitudinal waves (sound) oscillate parallel. Electromagnetic waves are transverse and travel at c = 3.00 × 10^8 m s^-1 in a vacuum.
- Reflection: angle of incidence equals angle of reflection, measured from the normal. Refraction: n1 sinθ1 = n2 sinθ2. Refractive index n = c/v.
- Total internal reflection occurs only from higher to lower refractive index. Critical angle: sinθc = n2/n1.
- Superposition adds displacements. Interference depends on path difference and phase. Standing waves have nodes and antinodes; adjacent nodes are λ/2 apart.
- Diffraction is spreading around obstacles or through gaps; it is greatest when the gap is comparable to λ. The Doppler effect changes observed frequency when source and observer have relative motion.
Worked example
Light in air (n = 1.00) strikes water (n = 1.33) at 40° to the normal. Find the angle of refraction and the speed in water. Snell's law: 1.00 sin40° = 1.33 sin r, so sin r = 0.483 and r = 28.9°. Speed v = c/n = 3.00 × 10^8 / 1.33 = 2.26 × 10^8 m s^-1.
Traps
Measure angles from the normal, not the surface. Check the calculator is in degree mode. Do not change frequency during refraction. The critical angle formula is only valid when n1 > n2. For standing waves, do not confuse node spacing with wavelength.