C. Wave behaviour

• Conditions that lead to simple harmonic motion.

• SHM defining equation: a = -ω^2x.

• Describe SHM using T, f, ω, amplitude, equilibrium position and displacement.

• Oscillation period relations: T=1/f=2π/ω.

• The time period of a mass–spring system is T=2π√(m/k).

• The time period of a simple pendulum in the small-angle approximation is T=2π√(l/g).

• Describe qualitatively how kinetic and potential energy change during one cycle of an oscillation; total mechanical energy remains constant for an ideal oscillator.

• HL: include phase angle in SHM descriptions.

• HL: solve SHM with x=x0 sin(ωt) and v=v0 cos(ωt).

• Distinguish transverse and longitudinal travelling waves by comparing particle or field oscillation with the direction of propagation and energy transfer. • Describe the motion of particles in a medium using displacement with position and with time.

• Apply wavelength λ, frequency f, time period T and wave speed v to wave motion using v=fλ=λ/T.

• Explain sound as a mechanical longitudinal wave, including particle oscillations, compressions and rarefactions, and energy transfer through a medium.

• Explain electromagnetic waves as transverse oscillating electric and magnetic fields that can propagate through a vacuum. • Use the approximate wavelength orders of magnitude in the Physics data booklet without treating them as sharp boundaries.

• Compare mechanical waves, which require a medium, with electromagnetic waves, which can travel through a vacuum. • Travelling waves transfer energy even when there is no resultant displacement of the medium. • Apply the wave model to both mechanical and electromagnetic waves.

• Waves travelling in two and three dimensions can be described through the concepts of wavefronts and rays.

• Snell’s law: n1 sinθ1 = n2 sinθ2.

• Refractive index: n=c/v.

• Total internal reflection condition uses critical angle: sinθc=n2/n1.

• Superposition adds displacements where waves overlap.

• Coherence requires constant phase difference between waves.

• Path difference determines constructive or destructive interference.

• Two-source interference depends on path difference and wavelength.

• Young double-slit spacing: s = λD/d.

• Explain wave behaviour at boundaries in terms of reflection, refraction and transmission. • Sketch and interpret incident, reflected and transmitted wavefronts and rays at normal or oblique incidence within the syllabus guidance.

• Explain diffraction around a body and through an aperture. • Use wavefront–ray diagrams to represent diffraction, and relate greater spreading qualitatively to wavelength and aperture size.

• Single-slit diffraction depends on slit width and wavelength.

• Single-slit diffraction envelope modulates double-slit interference.

• Diffraction grating maxima: nλ = d sinθ.

• Standing waves form by superposition of identical opposite-travelling waves.

• Identify nodes, antinodes, amplitude and phase along standing waves. • Include relative amplitude and phase difference along the standing wave.

• Know standing-wave patterns in strings and pipes.

• Resonance relates driving frequency, natural frequency and amplitude.

• Damping reduces maximum amplitude and shifts resonant frequency.

• Compare light, critical and heavy damping effects.

C.5.1—Doppler effect

• Nature of the Doppler effect for sound waves and electromagnetic waves.

C.5.2—Doppler wavefront diagrams

• Represent Doppler effect with wavefront diagrams for moving source or observer.

C.5.3—Light Doppler approximation

• For light at low relative speed: Δf/f = Δλ/λ ≈ v/c.

C.5.4—Spectral line shifts

• Spectral line shifts reveal motion of stars and galaxies.

C.5.5 (HL)—Mechanical-wave Doppler formulas

• HL: Doppler formulas for sound/mechanical waves. • Distinguish moving-source and moving-observer cases.