Wave Motion: Complete A Level H2 Physics Cheatsheet
A Level Physics (H2), Chapter 10 · 9478 Topic 10 · Read time: ~10 minutes
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Key Formulas
Mechanical and electromagnetic waves
Mechanical waves are oscillations of particles in a material medium, such as a string, water or air. Electromagnetic waves are oscillations of electric and magnetic fields, and need no medium.
A progressive wave transfers energy without transferring matter.
Terms: displacement, amplitude, period, frequency, wavelength, speed, phase and phase difference. From speed = distance/time over one period, v = λ/T = fλ.
Reading wave graphs
A displacement-distance graph is a snapshot at one instant. Read the wavelength from it.
A displacement-time graph follows one particle. Read the period from it.
For longitudinal waves the displacement is along the direction of travel. On a displacement-distance graph, a compression is where neighbouring particles are displaced towards each other.
Two points one wavelength apart are in phase. Half a wavelength apart, they are in antiphase (phase difference π).
Trap: To find the direction a particle moves next on a displacement-distance graph, sketch the wave shifted slightly forward in the direction of travel and see whether that point goes up or down.
Intensity and the inverse square law
Intensity is the power transferred per unit area, I = P/A, in W m⁻². It is proportional to amplitude squared.
From a point source with no energy loss, power spreads over a sphere, so I = P/4πr². Doubling the distance quarters the intensity and halves the amplitude.
Trick: Chain the two relationships: I ∝ 1/r² and I ∝ A², so A ∝ 1/r.
Polarisation
Polarisation restricts the oscillations to one plane. Only transverse waves can be polarised, so polarisation is evidence that light is transverse. Sound cannot be polarised.
Plane-polarised light passing through a polarising filter at angle θ to its plane of polarisation keeps amplitude A₀ cos θ and intensity I = I₀ cos²θ (Malus' law).
Unpolarised light through one ideal polariser loses half its intensity.
Trap: Amplitude uses cos θ, intensity uses cos²θ. Mixing them up is the most common Malus' law error.
Worked Example
A small loudspeaker emits sound uniformly in all directions with an output power of 0.80 W.
(a) Calculate the intensity 2.0 m from the speaker. [2]
I = P / 4πr² = 0.80 ÷ (4π × 2.0²)
= 1.6 × 10⁻² W m⁻²
(b) At 4.0 m, state the intensity and the ratio of amplitudes compared with 2.0 m. [2]
Doubling r quarters I: 4.0 × 10⁻³ W m⁻²
A ∝ 1/r, so the amplitude halves (ratio 1 : 2)
(c) Plane-polarised light of intensity 12 W m⁻² passes through a polariser at 60° to its plane of polarisation. Calculate the transmitted intensity. [2]
I = I₀ cos²θ = 12 × cos² 60°
= 12 × 0.25 = 3.0 W m⁻²
Why this question is a good test of the topic: it checks the inverse square law, the link from intensity to amplitude, and the squared cosine in Malus' law, three places where students often forget to square or square-root.
Frequently Asked Questions
What is the difference between mechanical and electromagnetic waves?
Mechanical waves are oscillations of particles in a medium. Electromagnetic waves are oscillating electric and magnetic fields and need no medium.
How is intensity related to amplitude?
Intensity is proportional to amplitude squared. Doubling the amplitude gives four times the intensity.
Why does intensity follow an inverse square law?
The power from a point source spreads over a sphere of area 4πr², so intensity falls as 1/r².
Why can't sound be polarised?
Polarisation only applies to transverse waves. Sound is longitudinal.
What is Malus' law?
The transmitted intensity of plane-polarised light through a polariser is I = I₀ cos²θ, where θ is the angle between the plane of polarisation and the polariser's axis.
Wave graphs and intensity questions costing marks?
Small group A Level H2 Physics classes at TGC Academy's Bishan, Bukit Timah and Potong Pasir centres, helmed by Andrew Seah, MOE Award-Winning Teacher and Marshall Cavendish textbook author, with a team of tutors.