Name: Eclat Institute - Orchard Physics Practical Lab
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H2 Physics Superposition Notes | A-Level 9478

(a) explain and use the principle of superposition in simple applications.
(b) show an understanding of experiments which demonstrate standing (stationary) waves using microwaves, stretched strings and air columns.
(c) explain the formation of a standing (stationary) wave using a graphical method, and identify nodes and antinodes, differentiating between pressure and displacement nodes and antinodes for sound waves.
(d) determine the wavelength of sound using standing (stationary) waves.
(e) show an understanding of the terms diffraction, interference, coherence, phase difference and path difference.
(f) show an understanding of phenomena which demonstrate two-source interference using water waves, sound waves, light and microwaves.
(g) show an understanding of the conditions required for two-source interference fringes to be observed.
(h) recall and use the equation $\dfrac{ax}{D} = \lambda$ to solve problems for double-slit interference, where $a$ is the slit separation and $x$ is the fringe separation.
(i) recall and use the equation $a \sin\theta = n\lambda$ to solve problems involving the principal maxima of a diffraction grating, where $a$ is the slit separation.
(j) describe the use of a diffraction grating to determine the wavelength of light (knowledge of the structure and use of a spectrometer is not required).
(k) show an understanding of phenomena which demonstrate diffraction through a single slit or aperture, or across an edge, such as the diffraction of water waves in a ripple tank with both a wide gap and a narrow gap, or the diffraction of sound waves from loudspeakers or around corners.
(l) recall and use the equation $b \sin\theta = \lambda$ to solve problems involving the positions of the first minima for diffraction through a single slit of width $b$ .
(m) recall and use the Rayleigh criterion $\theta \approx \dfrac{\lambda}{b}$ for the resolving power of a single aperture, where $b$ is the width of the aperture.

Question clue	Route to use	First move	Common trap
Two disturbances overlap at a point	resultant displacement	add signed displacements at that instant	adding amplitudes without checking phase
Fixed nodes and antinodes appear	standing wave	mark node spacing as $\lambda/2$	thinking the stationary pattern transfers energy along itself
Bright and dark fringes from two coherent sources	two-source interference	convert path difference to constructive or destructive condition	confusing phase difference with path difference
Many slits produce sharp maxima	diffraction grating	use $a\sin\theta=n\lambda$ and check possible orders	allowing impossible orders with $\sin\theta>1$
A single slit or aperture gives a broad central maximum	single-slit diffraction or resolution	identify slit width or aperture diameter $b$	using the double-slit fringe formula

Medium	Demo	Why parents should care
Microwave oven	Take out the turntable, melt chocolate, measure node spacing to estimate $\lambda$ and hence $c$	Turns kitchen fun into physics; reinforces node-spacing = $\dfrac{\lambda}{2}$
Stretched string	Vibrator + pulley illustrates harmonics; count antinodes to read $n$	Many WA questions hide “find mode number” marks here
Closed air column	Slide a piston to find loud spots (pressure antinodes)	Links sound labs to displacement vs pressure phase diagrams

Given clue	Convert to	Use this condition	Watch for
Path difference is stated directly	Compare it with $\lambda$ .	Bright: $n\lambda$ ; dark: $(n+\tfrac12)\lambda$ .	Calling any non-zero path difference destructive.
Phase difference is stated	Convert using $\phi = 2\pi \Delta r / \lambda$ .	Bright: phase difference is a whole multiple of $2\pi$ ; dark: odd multiple of $\pi$ .	Forgetting that $\pi$
Screen position $x$ is given	Use $\Delta r \approx ax/D$ .	Then test the path difference condition.	Using $x$ as though it is already a path difference.
Fringe spacing changes	Use $\Delta x = \lambda D/a$ .	Larger $\lambda$ or $D$ gives wider fringes; larger $a$ gives closer fringes.	Reversing the slit-separation effect.

Question cue	First move	What to reject
Lines per metre or lines per millimetre are given	Convert to slit spacing with $a = 1/N$ .	Using the line density directly as $a$ .
Maximum order is asked	Use $n\lambda \leq a$ .	Any whole-number order with $n\lambda > a$ .
Angle for a named order is asked	Substitute into $a\sin\theta = n\lambda$ .	Answers where $\sin\theta > 1$ .
White light is used	Longer wavelengths diffract more for the same order.	Saying violet is always farther from the centre than red.

Situation	Width symbol	What a larger width does	Common trap
Single slit, first minimum	$b$ in $b\sin\theta = \lambda$	Smaller $\theta$ , so the central maximum narrows.	Saying a wider slit spreads the pattern more.
Circular aperture, resolution	$b$ in $\theta \approx 1.22\lambda/b$	Smaller minimum angular separation, so two close sources are easier to resolve.	Treating a smaller $\theta$ as worse because the number is smaller.
Same aperture, longer wavelength	$\lambda$ increases	Larger diffraction angle and poorer resolution.	Comparing colours or waves without checking wavelength.

H2 Physics Superposition Notes | A-Level 9478

Concrete example: how to use this page

Decision map - choose the superposition route first

1 Where this sits in the syllabus

2 Principle of superposition

2.1 Quick check

2.2 Mini-drill

3 Standing waves

3.1 Graphical formation

3.2 Measuring sound wavelength

4 Two-source interference

4.1 Double-slit formula

Path-difference checkpoint

5 Diffraction grating

Grating order checkpoint

6 Single-slit diffraction

7 Rayleigh criterion - resolving power

Aperture width checkpoint

8 Three common exam traps

9 WA timing rules (tested in our tuition drills)

Comprehensive revision pack

9478 Section III, Topic 11 Syllabus outcomes

Concept map (in words)

Key relations

Derivations & reasoning to master

Worked example 1 - string harmonics

Worked example 2 - diffraction grating spectrum

Practical & data tasks

Common misconceptions & exam traps

Quick self-check quiz

Revision workflow

Practice Quiz

10 Further reading

11 Call-to-action

Related Posts

Context	Expression
Resultant of equal waves	$y = 2A \cos\Bigl( \dfrac{\phi}{2} \Bigr) \sin\Bigl( \omega t + \dfrac{\phi}{2} \Bigr)$
Standing wave nodes	$\Delta x = \dfrac{\lambda}{2}$
Young's double slit	$\dfrac{a x}{D} = n \lambda$
Diffraction grating	$a \sin \theta = n \lambda$
Single-slit diffraction	$b \sin \theta = m \lambda$ (first minimum $m = 1$ )
Rayleigh criterion	$\theta = 1.22 \dfrac{\lambda}{b}$
Pipe harmonics (open/closed)	$L = n \dfrac{\lambda}{2}$ (open), $L = (2n - 1) \dfrac{\lambda}{4}$

Symbol / term	Meaning
$\phi$	Phase difference between the interfering waves
$A$	Amplitude of each interfering wave
$\omega, t$	Angular frequency and time
$\Delta x$	Separation between successive displacement nodes
$\lambda$	Wavelength of the wave
$a$	Slit separation or grating spacing
$x$	Fringe spacing on the observation screen
$D$	Distance from the slits/grating to the screen
$b$	Slit width / aperture diameter (single slit or telescope)
$n, m$	Order numbers ( $n$ for maxima, $m$ for minima)
$\theta$	Diffraction / interference angle
$L$	Length of the air column or string segment