§ 7.1 Progressive waves
Key ideas
- A progressive wave transfers energy without transferring matter.
- Amplitude: maximum displacement from equilibrium. Wavelength λ: distance for one complete cycle. Period T: time for one cycle. Phase difference compares two points' stages of oscillation (one whole wavelength = 360°).
- A displacement-distance graph shows λ directly; a displacement-time graph shows T directly.
- Intensity is power per unit area, and intensity is proportional to amplitude squared.
Equations
v = f λwave speed = frequency × wavelengthm s⁻¹
f = 1 / Tfrequency is the reciprocal of the periodHz
I = P / Aintensity = power ÷ area, with I ∝ amplitude²W m⁻²
Fig. 1 · The same wave plotted two ways: against distance the repeat length is λ; against time the repeat is the period T; the amplitude A is read from the equilibrium line either way.
Watch out: check the horizontal axis before reading a wave graph. The crest-to-crest spacing is λ only on a distance axis; on a time axis it is the period T.
§ 7.2 Transverse and longitudinal waves
Key ideas
- Transverse: oscillations perpendicular to the energy travel (light, all EM waves, waves on strings).
- Longitudinal: oscillations parallel to the travel (sound), forming compressions and rarefactions.
- Only transverse waves can be polarised; this is the experimental test that distinguishes the two.
Watch out: a displacement-distance graph of a longitudinal wave still looks sinusoidal: the graph plots displacement along the travel direction. A sine-shaped graph does not prove a wave is transverse.
§ 7.3 Doppler effect for sound waves
Key ideas
- When a sound source moves, the wavefronts bunch together ahead of it and stretch behind it; the wave speed in the air is unchanged.
- An observer ahead of an approaching source hears a higher frequency; behind a receding source, a lower one.
Equations
fo = fs v / (v ∓ vs)minus for approach (higher f), plus for recession (lower f)Hz
Fig. 2 · Each wavefront is centred where the source was when it was emitted, so the spacing shrinks ahead and grows behind: the observed frequency shifts.
Watch out: the sign lives in the denominator. Approaching means v − vs (smaller denominator, higher fo). If your "approaching" answer comes out lower than fs, the sign went the wrong way.
§ 7.4 Electromagnetic spectrum
Key ideas
- Order of increasing frequency: radio, microwaves, infrared, visible, ultraviolet, X-rays, gamma.
- All EM waves are transverse and travel at the same speed in free space (and approximately in air).
- Visible light spans roughly 400 nm (violet) to 700 nm (red).
Equations
c = 3.0 × 10⁸ m s⁻¹the speed of every EM wave in free spacem s⁻¹
Watch out: wavelength boundaries are worth memorising in metres: 400 nm = 4 × 10⁻⁷ m. Slipping a power of ten when converting nm is the usual way to lose this mark.
§ 7.5 Polarisation
Key ideas
- A polarised wave oscillates in one plane only; polarisation is possible for transverse waves and impossible for longitudinal ones.
- A polarising filter transmits the component of the oscillation along its axis; a second filter (the analyser) at angle θ cuts the intensity by cos²θ.
- Crossed filters (θ = 90°) transmit nothing.
Equations
I = I0 cos²θMalus's law: transmitted intensity through the analyserW m⁻²
Fig. 3 · The polariser selects one plane; the analyser then passes only the component along its own axis, so the intensity falls to I0 cos²θ.
Watch out: cos²θ applies to intensity; the amplitude falls by cos θ. At θ = 60° the amplitude halves but the intensity drops to a quarter.