LucidSTEM
A-LEVEL 9702 · AS · TOPIC 8
Superposition
The chain of the topic: one principle, that meeting waves add displacement by displacement, builds into stationary waves, then diffraction at a gap, then two-source interference, and finally the diffraction grating. Around the hexagon are the four ideas; above is what it builds on, below is where it leads.
TOPIC 8: SUPERPOSITION
CAMBRIDGE A-LEVEL PHYSICS 9702 · PATHWAYS
TheLucidSTEM · thelucidstem.com
BUILDS ON
T7 Waves: v = fλ, phase & wavelength T1 Quantities: phase angle in radians 8.1
8.2
8.3
8.4
TOPIC 8
SUPER-
POSITION
y = y₁ + y₂
1 · STATIONARY WAVES
Two equal waves, opposite directions, trapped.
Superposition: where waves meet, displacements add.
Incident plus reflected wave gives fixed nodes (N)
and antinodes (A); no net energy travels along it.
Adjacent nodes are half a wavelength apart.
node to node = λ / 2
N
N
A
A
λ/2
nodes stay still; antinodes swing
2 · DIFFRACTION
Waves spread out on passing through a gap.
Every wave bends around obstacles and edges.
Spreading is greatest when the gap width is about
equal to the wavelength λ.
Wavelength and frequency are unchanged.
gap ≈ λ → widest spread
plane
a narrow gap spreads the wave out
3 · TWO-SOURCE INTERFERENCE
Coherent sources build a fixed fringe pattern.
Coherent: constant phase difference, same λ.
Path difference = nλ gives constructive (bright);
= (n + ½)λ gives destructive (dark).
Young's double slit fixes λ from the fringe spacing x.
λ = a x / D
a: slit gap D: slit-to-screen
x
2 slits
screen
D
4 · THE DIFFRACTION GRATING
Many slits sharpen the maxima into orders.
Slit spacing d (from lines per metre); n is the order.
Maxima are bright and far apart, so λ is precise.
White light splits into spectra: each λ at its own θ.
d sinθ = nλ
n = 0, 1, 2, ...
θ
n = +1
n = 0
n = −1
grating
LEADS TO
T22 Quantum physics: electron diffraction shows wave nature T25 Astronomy: gratings split starlight to read redshift Each reuses one idea: waves that overlap reveal λ, and from λ we read out matter, light and the speed of distant galaxies.
← Builds on IGCSE: General wave properties