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C. Wave behaviour

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  1. C.1 Simple harmonic motion

    1. • Conditions that lead to simple harmonic motion.

    2. • SHM defining equation: a = -ω^2x.

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

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

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

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

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

    8. • HL: include phase angle in SHM descriptions.

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

  2. C.2 Wave model

    1. • 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.

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

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

    4. • 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.

    5. • 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.

  3. C.3 Wave phenomena

    1. C.3.1—Wavefronts and rays

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

    2. C.3.2—Snell’s law

      • Snell’s law: n1 sinθ1 = n2 sinθ2.

    3. C.3.3—Refractive index

      • Refractive index: n=c/v.

    4. C.3.4—Total internal reflection

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

    5. C.3.5—Superposition

      • Superposition adds displacements where waves overlap.

    6. C.3.6—Coherence

      • Coherence requires constant phase difference between waves.

    7. C.3.7—Path difference

      • Path difference determines constructive or destructive interference.

    8. C.3.8—Two-source interference

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

    9. C.3.9—Young double-slit equation

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

    10. C.3.10—Reflection, refraction and transmission at boundaries

      • 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.

    11. C.3.11—Diffraction around bodies and through apertures

      • 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.

    12. C.3.12 (HL)—Single-slit diffraction

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

    13. C.3.13 (HL)—Diffraction envelope

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

    14. C.3.14 (HL)—Diffraction gratings

      • Diffraction grating maxima: nλ = d sinθ.

  4. C.4 Standing waves and resonance

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

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

    3. • Know standing-wave patterns in strings and pipes.

    4. • Resonance relates driving frequency, natural frequency and amplitude.

    5. • Damping reduces maximum amplitude and shifts resonant frequency.

    6. • Compare light, critical and heavy damping effects.

  5. C.5 Doppler effect

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

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

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

    4. • Spectral line shifts reveal motion of stars and galaxies.

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