Topic 3 of 8 · Form 5
Waves and superposition
Transverse and longitudinal waves; displacement, amplitude, phase difference, period, frequency, wavelength, speed (v = fλ); intensity ∝ amplitude² and I = P/A; the Doppler effect for sound: f₀ = fₛv/(v ± vₛ).
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Progressive waves
Transverse and longitudinal waves; displacement, amplitude, phase difference, period, frequency, wavelength, speed (v = fλ); intensity ∝ amplitude² and I = P/A; the Doppler effect for sound: f₀ = fₛv/(v ± vₛ).
Electromagnetic spectrum and polarisation
Wavelength ranges; all EM waves travel at 3.00 × 10⁸ m s⁻¹ in a vacuum; Malus's law I = I₀cos²θ.
Superposition
Stationary waves (nodes, antinodes, distance λ/2 between nodes); diffraction; interference and coherence; Young's double slit: λ = ax/D; diffraction grating: d sin θ = nλ.
Worked example: Light of wavelength 600 nm passes through slits 0.40 mm apart onto a screen 2.0 m away. Find the fringe spacing.
x = λD/a = (600 × 10⁻⁹ × 2.0)/(0.40 × 10⁻³) = 3.0 × 10⁻³ m = 3.0 mm
Worked example: A grating has 500 lines per mm. Find the highest order visible with light of wavelength 550 nm.
d = 2.0 × 10⁻⁶ m; n ≤ d/λ = 3.6 → highest order 3
Check yourself
- A source emitting 500 Hz approaches an observer at 20 m s⁻¹. Speed of sound 340 m s⁻¹. Find the observed frequency.
- Polarised light of intensity I₀ passes through a polariser at 60°. What fraction is transmitted?
- What is the distance between adjacent nodes in a stationary wave of wavelength 0.8 m?
Show answers
- 500 × 340/320 = 531 Hz
- cos²60° = ¼
- 0.4 m
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