Wave Behaviours¶
Syllabus mapping
PY-11-02 — Waves. Covers: the law of reflection; wavefront and ray diagrams; refraction, refractive index and Snell's law; total internal reflection and the critical angle; diffraction; superposition and interference; standing waves; the Doppler effect for sound and light.
Wording above is paraphrased for teaching use — cross-check against the official syllabus PDF (see Resources) before treating any line as verbatim NESA text.
You need to know: the law of reflection, Snell's law and the critical angle for refraction, how diffraction and interference arise from superposition, what a standing wave is, and how the Doppler effect shifts frequency.
Assumed knowledge check¶
Before this page makes sense, you should be comfortable with:
- Wave Properties — wavelength, frequency, the wave equation
- Trigonometry — SOH-CAH-TOA
Core¶
Law of reflection¶
The angle of incidence equals the angle of reflection, both measured from the normal (the line perpendicular to the reflecting surface at the point of contact) — not from the surface itself. This is the single most common labelling mistake on ray diagrams.
🖼️ Diagram needed: wavefront and ray diagrams for reflection and refraction, all angles clearly measured from the normal. TODO — placeholder until sourced/drawn.
Refraction and refractive index¶
When a wave crosses into a new medium, its speed changes (frequency stays fixed — see Wave Properties), which bends its direction of travel unless it hits the boundary straight-on. The refractive index of a medium:
— the ratio of the speed of light in vacuum to its speed in medium \(x\). A higher refractive index means light travels slower in that medium.
Snell's law relates the angles either side of a boundary:
Worked example
Light travels from air (\(n_1 = 1.00\)) into glass (\(n_2 = 1.50\)) at an angle of incidence of \(40^\circ\). Find the angle of refraction.
Light bends towards the normal going into the denser (higher-\(n\)) medium — consistent with slowing down.
Total internal reflection and the critical angle¶
Going the other way — from a denser medium into a less dense one (e.g. glass into air) — light bends away from the normal. Past a certain angle of incidence, the refracted ray would need to bend more than \(90^\circ\), which is impossible: instead, all the light reflects back into the denser medium. This is total internal reflection, and it starts at the critical angle:
where \(n_1\) is the denser (higher-index) medium the light starts in.
Worked example
Find the critical angle for light travelling from glass (\(n_1=1.50\)) into air (\(n_2=1.00\)).
Beyond \(41.8^\circ\), light hitting that glass–air boundary from inside the glass reflects entirely back in — none escapes into the air.
Diffraction¶
Diffraction is the bending/spreading of waves around obstacles or through openings — most noticeable when the opening or obstacle is comparable in size to the wavelength. For a diffraction grating or double slit:
where \(d\) is the slit spacing, \(\theta\) the angle to a bright fringe, \(m\) the order (an integer), \(y\) the fringe position on a screen, and \(L\) the distance to the screen.
Superposition and interference¶
When two or more waves overlap, their displacements add algebraically at every point (superposition). This produces:
- Constructive interference — waves in phase, displacements add, resulting amplitude is larger
- Destructive interference — waves out of phase, displacements subtract, resulting amplitude is smaller (or zero, if the waves are otherwise identical)
Standing waves¶
When two waves of the same frequency travel in opposite directions through the same medium (e.g. a wave and its own reflection), they superpose into a standing wave — a pattern that oscillates in place rather than travelling. Nodes are points of permanently zero displacement; antinodes are points of maximum oscillation, exactly halfway between adjacent nodes.
The Doppler effect¶
Frequency shifts higher when source and observer approach each other, and lower when they move apart. Sign convention: velocities are positive when moving towards the other party, negative when moving away — get this wrong and the shift comes out backwards.
Worked example
An ambulance siren emits at \(700\ \text{Hz}\) and approaches a stationary listener at \(30\ \text{m s}^{-1}\). Speed of sound: \(340\ \text{m s}^{-1}\) (from your data sheet). Find the frequency heard.
Observer stationary (\(v_{observer}=0\)), source approaching (\(v_{source}=+30\ \text{m s}^{-1}\), positive since moving towards the observer):
Practical¶
Suggested prac: refractive index of a material — shine a ray through a glass or perspex block, measure angles of incidence and refraction for several trials, and calculate \(n\) via Snell's law (or plot \(\sin\theta_1\) vs \(\sin\theta_2\) for a more reliable line-of-best-fit value). TODO — link this school's actual prac instructions once written.
Advanced
Optical fibres rely entirely on total internal reflection — light is kept inside a fibre by ensuring it always strikes the fibre's internal wall beyond the critical angle, letting it travel long distances with minimal loss.
Diffraction grating problems with multiple orders — the same \(d\sin\theta = m\lambda\) equation, applied for \(m = 1, 2, 3, ...\) to find the angle of each successive bright fringe.
Standing waves on a string fixed at both ends must have a node at each end, which restricts the wavelengths that fit: the fundamental has length \(L = \dfrac{\lambda}{2}\), and higher harmonics fit progressively more half-wavelengths into the same length.
Extension
Beyond the Physics 11–12 syllabus — won't appear in the HSC, included for interest / depth study inspiration.
📎 Depth study idea
The Doppler effect for light works the same way conceptually as for sound, but relativistic effects matter at the speeds involved — this is exactly the mechanism behind cosmological redshift, where light from a receding galaxy is stretched to longer (redder) wavelengths. This is picked up properly in Year 12's Nature of Light focus area, but a depth study now could explore the qualitative link between what's covered here (Doppler shift for sound) and how astronomers use the same principle to measure galaxies moving away from us — genuinely one of the more famous applications of a Year 11 concept in modern physics.
Video/visual resources¶
- 🖥️ PhET Simulation — Wave Interference — TODO: confirm current PhET link (flagged in
project.mdSection 7 as strongly recommended for diffraction/interference) - 🎥 Khan Academy — TODO: source a refraction/Snell's law explainer
- 🎥 Physics High — TODO: check for a NSW-syllabus-aligned wave behaviours video
Check yourself¶
-
Light travels from air (\(n=1.00\)) into water (\(n=1.33\)) at \(50^\circ\) to the normal. Find the angle of refraction.
Answer
\(\sin\theta_2 = \dfrac{1.00 \times \sin50^\circ}{1.33} \approx 0.576 \implies \theta_2 \approx 35.2^\circ\)
-
Find the critical angle for light travelling from a medium with \(n=1.60\) into air (\(n=1.00\)).
Answer
\(\sin\theta_c = \dfrac{1.00}{1.60} = 0.625 \implies \theta_c \approx 38.7^\circ\)
-
A car horn (\(500\ \text{Hz}\)) approaches a stationary pedestrian at \(20\ \text{m s}^{-1}\), then after passing, moves away at the same speed. Find the frequency heard (a) as it approaches, and (b) as it recedes. Speed of sound: \(340\ \text{m s}^{-1}\).
Answer
(a) Approaching, \(v_{source}=+20\): \(f' = 500\left(\dfrac{340}{340-20}\right) = 500\left(\dfrac{340}{320}\right) \approx 531\ \text{Hz}\)
(b) Receding, \(v_{source}=-20\): \(f' = 500\left(\dfrac{340}{340+20}\right) = 500\left(\dfrac{340}{360}\right) \approx 472\ \text{Hz}\)