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A-Level The superposition principle, standing waves, interference and single-slit diffraction
What the A-Level syllabus expects for The superposition principle, standing waves, interference and single-slit diffraction, and how to practise it.
What the syllabus expects
- Set out the principle of superposition and apply it in basic cases
- Understand the experiments that reveal stationary waves with microwaves, taut strings and air columns
- Use a graphical method to explain how a stationary wave builds, mark its nodes and antinodes, and for sound tell pressure nodes and antinodes apart from displacement ones
- Find the wavelength of sound by means of stationary waves
- Understand this cluster of ideas: coherence, path difference, phase difference, interference and diffraction
- Understand the effects that showcase interference from two sources across water waves, sound, light and microwaves
- Know what has to hold for interference fringes from two sources to become visible
- Apply the double-slit relation λ = ax/D in problems
Scope: here a is the slit spacing and x the fringe spacing - Use a sinθ = nλ for the principal maxima of a diffraction grating
Scope: a denotes the slit spacing - Explain how a diffraction grating pins down the wavelength of light
Scope: the spectrometer's construction and use are not required - Understand the situations that display diffraction at a single slit, an aperture or an edge, for example ripple-tank water waves passing wide and narrow gaps, or sound spreading from speakers and bending round corners
- Apply b sinθ = λ to locate the first minima of single-slit diffraction
Scope: b is the width of the slit - Use the Rayleigh criterion θ ≈ λ/b for how finely a single aperture can resolve detail
Scope: b is the aperture width
How it's examined
Questions on this topic most often ask you to describe, estimate, find, show. About 7% of the past-paper style questions in Rae's bank for this subject sit in this topic.
Worked examples
Example 1 (3 marks)
(a) Two loudspeakers, M and N, are driven together in phase at equal amplitude and at a frequency of 680 Hz. A point Q lies 18.0 m from M and 20.25 m from N. Sound travels at 340 m s⁻¹. (i) Show that the sound heard at Q has minimum intensity.
Show the worked answer
Wavelength: λ = v/f = 340/680 = 0.50 m. Path difference: NQ − MQ = 20.25 − 18.0 = 2.25 m. In wavelengths: 2.25 / 0.50 = 4.5 = 4½ wavelengths = 9 half-wavelengths. This is an odd number of half-wavelengths, so the two waves arrive exactly in antiphase and interfere destructively, giving minimum (ideally zero) intensity at Q.
Example 2 (4 marks)
(b) Light emitted by a sodium discharge lamp falls normally on a diffraction grating that has 6.00 × 10⁵ lines per metre. Its spectrum includes a closely spaced yellow doublet with wavelengths 589 nm and 590 nm. (i) Find the angular separation between these two lines as seen in the second order spectrum.
Show the worked answer
Grating spacing d = 1/(6.00x10⁵) = 1.667x10⁻⁶ m. Second order: d sin(theta) = 2*lambda. For 589 nm: sin(theta1) = 2*589x10⁻⁹/1.667x10⁻⁶ = 0.7068, theta1 = 44.98 deg. For 590 nm: sin(theta2) = 2*590x10⁻⁹/1.667x10⁻⁶ = 0.7080, theta2 = 45.07 deg. Angular separation = theta2 - theta1 = 0.097 deg (about 1.7x10⁻³ rad).
Example 3 (2 marks)
(iii) With both loudspeakers switched on, the sound intensity measured at point Q equals I₀. Loudspeaker B is then switched off, while loudspeaker A keeps producing sound of the same amplitude and frequency. The intensity at Q now becomes I_A. Work out an estimate for the ratio I_A / I₀.
Show the worked answer
Point Q is a point of constructive interference, where the two waves of equal amplitude a arrive in phase, giving a resultant amplitude of 2a. Intensity is proportional to amplitude squared, so with both speakers on I₀ ∝ (2a)² = 4a². With B switched off, only A contributes amplitude a, so I_A ∝ a². Hence I_A/I₀ = a²/(4a²) = 1/4.
More worked questions on this topic
- (ii) A microphone is moved steadily along the straight line joining P to Q, where PQ is perpend (2 marks)
More A-Level H2 Physics topics
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