Progressive waves, polarisation and the EM spectrum
8 min read · about 1 h 40 min with practice3 quick checks≈2% of the testFoundational: Foundational: the groundwork the rest of the unit builds on
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Progressive waves are the vocabulary of the whole waves unit: most waves questions open with a definition, a v=fλ calculation or a graph to read. The marks that separate an A from an A* come from phase difference, reading the right kind of graph, and explaining polarisation with precise physics rather than a “slots in a fence” analogy.
By the end you’ll be able to
Define amplitude, wavelength, frequency, period, phase and phase difference (in degrees and radians) and use v = fλ
Distinguish transverse and longitudinal waves and explain why only transverse waves can be polarised
Describe applications of polarisation (Polaroid, aerial alignment, stress analysis) and apply Malus’s law where required
Relate intensity to power per unit area and to amplitude squared
Recall the order and approximate wavelengths of the electromagnetic spectrum, and interpret oscilloscope traces of waves
The first 3 of 11 cards for this topic. Sign in and finish the lesson to review them with spaced repetition.
PromptCard 1 of 3
Define the amplitude of a wave.
λ
Convert a separation into a phase difference in degrees, radians or fractions of a cycle.
Tell displacement–distance graphs from displacement–time graphs, and find compressions and rarefactions on a graph of a longitudinal wave.
Explain why polarisation shows a wave is transverse, and describe applications: Polaroid, aerial alignment, microwave grilles and stress analysis.
Recall the order and approximate wavelengths of the electromagnetic spectrum.
Relate intensity to power per unit area and to amplitude squared.
Core ideas
The vocabulary, done precisely
Term
Meaning
Unit
Displacement
distance and direction of a point from its equilibrium position
m
Amplitude A
maximum displacement from the equilibrium position
m
Wavelength λ
minimum distance between two points oscillating in phase (e.g. crest to crest)
m
Period T
time for one complete oscillation of a point
s
Frequency f
number of complete oscillations per second, f=1/T
Hz
Wave speed v
distance travelled by the wave (by its energy) per unit time
m s⁻¹
Phase difference Δϕ
how far one oscillation is ahead of or behind another, as a fraction of a cycle
rad or °
In one period the wave moves forward one wavelength, so v=λ/T=fλ. All electromagnetic waves travel at c=3.00×108 m s⁻¹ in a vacuum.
A progressive wave transfers energy without transferring the medium: each particle oscillates about a fixed equilibrium position.
Phase and phase difference
For two points a distance Δx apart along the direction of travel:
Δϕ=λ2πΔxrad=λ360°Δx
For two oscillations offset in time by Δt, Δϕ=2πΔt/T.
In phase: Δϕ=0,2π,4π,… (the points are a whole number of wavelengths apart).
Antiphase: Δϕ=π,3π,… (an odd number of half-wavelengths apart).
Quote the phase difference as an angle between 0 and 2π, and say which point leads if the question asks.
Two graphs that look identical
Displacement–distance graph
Displacement–time graph
What it shows
a snapshot of the whole wave at one instant
one point’s motion over time
Repeat length
wavelength λ
period T
Peak height
amplitude
amplitude
Always read the x-axis label first. To find which way a point is moving on a displacement–distance graph, imagine the whole curve shifted slightly in the direction of travel and see whether the point’s displacement goes up or down.
Transverse and longitudinal waves
Transverse: the oscillations are perpendicular to the direction of energy transfer. Examples: all EM waves (oscillating electric and magnetic fields), waves on a string, seismic S-waves.
Longitudinal: the oscillations are parallel to the direction of energy transfer, producing compressions and rarefactions. Examples: sound, ultrasound, seismic P-waves.
On a displacement–distance graph of a longitudinal wave (displacement to the right counted as positive), a compression is centred where the graph crosses zero with a negative gradient. The particles just behind that point have moved forward and those just ahead have moved back, so they crowd together. A rarefaction is at a zero crossing with a positive gradient. Points of maximum displacement are at normal pressure.
Polarisation
A wave is plane polarised when its oscillations are confined to a single plane that contains the direction of travel. Only transverse waves can be polarised: a longitudinal wave oscillates only along its direction of travel, so there is nothing to restrict. Polarising light therefore shows that light is transverse.
Polaroid filter: transmits the component of the electric field parallel to its transmission axis. Two filters with axes at 90° (“crossed”) block the light completely.
Microwave grille: a grid of metal rods absorbs the component of the electric field parallel to the rods, because the field drives electrons along them. It transmits the perpendicular component. This is the opposite of the “slots in a fence” picture and a favourite trap.
Aerials: radio and TV transmitters emit plane-polarised waves, so a receiving aerial’s rods must be aligned with the transmitter’s plane of polarisation (the electric field) for the strongest signal.
Polaroid sunglasses: light reflected from water or a wet road is partially polarised horizontally. Lenses with a vertical transmission axis absorb much of this glare.
Stress analysis: a plastic model between crossed polarisers shows coloured fringes that crowd together where stress is concentrated.
Malus’s law (Cambridge): when plane-polarised light of intensity I0 meets a filter whose axis is at θ to the plane of polarisation,
I=I0cos2θ
Apply it filter by filter. For unpolarised light, the first filter transmits half the intensity.
Intensity
I=AP(W m−2),I∝(amplitude)2
For a point source radiating uniformly, I=4πr2P, so the amplitude is proportional to 1/r.
The electromagnetic spectrum
Region
Approximate wavelength in a vacuum
Radio
longer than 10−1 m (up to kilometres)
Microwave
10−3 to 10−1 m
Infrared
7×10−7 to 10−3 m
Visible
4×10−7 to 7×10−7 m (400–700 nm)
Ultraviolet
10−8 to 4×10−7 m
X-ray
10−13 to 10−8 m
Gamma
shorter than about 10−11 m (overlaps X-rays; named by its nuclear origin)
As the wavelength decreases, the frequency and the photon energy increase.
Doppler effect for sound (Cambridge only)
When a source of frequency fs moves at speed vs relative to a stationary observer, the observed frequency is
fo=v∓vsfsv
Use the minus sign when the source approaches (the wavefronts bunch up, so the frequency rises) and the plus sign when it recedes.
Worked examples
Exam technique
Definitions only earn marks with the key idea: “maximum displacement from equilibrium”, “oscillations perpendicular to the direction of energy transfer”, “oscillations in one plane only”.
In oscilloscope questions, write T=(divisions per cycle)×(time-base) first, and convert ms to s before using f=1/T. Read across several cycles to reduce the uncertainty.
In phase questions, write the fraction Δx/λ first, then multiply by 2π or 360°. Always give the unit, and check the calculator is in degrees before using cos2θ.
In polarisation explanations, name what oscillates (the electric field, for EM waves) and its direction relative to the filter’s axis or the rods.
Common mistakes
Quick recap
v=fλ and f=1/T. All EM waves travel at c in a vacuum.
Δϕ=2πΔx/λ: whole wavelengths apart means in phase; odd half-wavelengths apart means antiphase.
A displacement–distance graph repeats every λ; a displacement–time graph repeats every T.
Transverse: oscillation perpendicular to energy transfer. Longitudinal: oscillation parallel to it.
Only transverse waves can be polarised, which is evidence that EM waves are transverse.
Metal grilles absorb the field component parallel to the rods; aerials are aligned with the field.