This mini-lesson covers Themes C.2–C.5 — Wave behaviour: the wave model and v = fλ, reflection & refraction (Snell's law), diffraction & interference, standing waves & resonance, and the Doppler effect.
Work through each screen, answer the questions as you go (some are reasoning, some are calculations) and collect ⭐ stars. Watch for the HL flag on higher-level extensions. Press Start when you're ready.
C.2 · the wave model
Describing waves
A wave transfers energy without transferring matter. Two types:
Transverse: oscillations are perpendicular to travel (light, water surface, waves on a string).
Longitudinal: oscillations are parallel to travel (sound, compression waves).
v = fλwave speed (m s⁻¹) = frequency (Hz) × wavelength (m)
Amplitude sets the energy; wavelength is the distance between adjacent in-phase points; frequency is set by the source and does not change when the wave enters a new medium.
Quick check
Quick check
?Sound travelling through air is which kind of wave?
Calculate
Calculate
#A wave has frequency 50 Hz and wavelength 6.0 m. Find its speed.
m s⁻¹
Hint: v = fλ = 50 × 6.0.
Calculate
Calculate
#A sound wave of frequency 170 Hz travels at 340 m s⁻¹. Find its wavelength.
m
Hint: λ = v ÷ f = 340 ÷ 170.
C.3 · refraction
Reflection, refraction & Snell's law
At a boundary a wave can reflect (angle in = angle out) and refract (change direction because its speed changes). The refractive index n = c ÷ v. Snell's law links the angles:
n₁ sinθ₁ = n₂ sinθ₂ · n = c ÷ vangles measured from the normal
Worked example — refractive index
Light travels at v = 2.0 × 10⁸ m s⁻¹ in a glass.
n = c ÷ v = 3.0 × 10⁸ ÷ 2.0 × 10⁸ = 1.5
Calculate
Calculate
#Light travels at 2.0 × 10⁸ m s⁻¹ inside a transparent block. Using c = 3.0 × 10⁸ m s⁻¹, find its refractive index.
Hint: n = c ÷ v = 3.0e8 ÷ 2.0e8.
Calculate
Calculate
#Light in air (n = 1.0) hits glass (n = 1.5) at 30° to the normal. Find the angle of refraction in the glass.
?When light passes from air into glass it slows down. How does the ray bend?
C.3 · interference
Diffraction & interference
Diffraction is the spreading of waves through a gap or around an edge — most pronounced when the gap is about one wavelength wide. When two coherent waves overlap they interfere:
s = λD ÷ dtwo-slit fringe spacing s, slit separation d, screen distance D
Young's double-slit experiment is the classic demonstration that light is a wave: bright and dark fringes appear where light adds or cancels.
Calculate
Calculate
#In a double-slit experiment λ = 600 nm, slit separation d = 0.50 mm, screen distance D = 2.0 m. Find the fringe spacing s, in mm.
mm
Hint: s = λD ÷ d = (600e-9 × 2.0) ÷ 0.50e-3 = 2.4e-3 m = 2.4 mm.
Sort it
Sort each item
Tap an item, then tap the group it belongs to.
↕️ Transverse wave
↔️ Longitudinal wave
📐 Wave quantity
C.4 · standing waves
Standing waves & resonance
A standing (stationary) wave forms when two identical waves travel in opposite directions (e.g. a wave and its reflection) and superpose. It has fixed nodes (no motion) and antinodes (maximum motion) — no net energy is transported.
String fixed at both ends: fundamental wavelength λ = 2L; harmonics at L, 2L/3, …
Resonance: driving a system at its natural frequency gives a large-amplitude standing wave.
Unlike a travelling wave, in a standing wave the nodes stay put and all points between two nodes oscillate in phase.
Quick check
Quick check
?Which statement about a standing wave on a string fixed at both ends is correct?
Match it
Match the phenomenon to its description
Tap a statement on the left, then its match on the right.
Statement
Answer
C.5 · Doppler
The Doppler effect
The Doppler effect is the change in observed frequency when a source and observer move relative to each other. An approaching source is heard at a higher pitch (waves bunched up); a receding source at a lower pitch.
f' = f × v ÷ (v ∓ v_s)moving source: − for approaching, + for receding
The same physics red-shifts light from galaxies moving away — key evidence for the expanding Universe. For sound it is the motion through the medium that matters.
C.5 · HL depth
Doppler equations & the grating
At HL you apply the Doppler equations quantitatively for a moving source and/or moving observer, and use the diffraction grating equation for sharp maxima:
d sinθ = nλgrating: d = slit spacing, n = order of the maximum
A grating with many slits gives much sharper, brighter maxima than two slits, so it measures wavelength precisely.
Calculate
Calculate
#HL: a siren emits 680 Hz and approaches you at 20 m s⁻¹; sound speed is 340 m s⁻¹. Find the observed frequency.
Hz
Hint: f' = f × v ÷ (v − v_s) = 680 × 340 ÷ (340 − 20).
Recap
The big ideas to know
Wave model: transfers energy not matter; v = fλ; transverse vs longitudinal
Refraction: n = c/v; Snell n₁sinθ₁ = n₂sinθ₂; slows & bends toward normal in denser medium
Interference: constructive nλ, destructive (n+½)λ; double slit s = λD/d
Standing waves: nodes & antinodes; resonance at natural frequency; no net energy transport
Doppler: approaching source → higher pitch; f' = fv/(v∓v_s)
That completes Wave Behaviour for IB Diploma Physics HL. Press Finish to see your score.
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