Revision summary

Identify the oscillating quantity, the graph's horizontal axis and the conditions of the model before selecting an equation.

Keep local motion separate from propagation

A mechanical wave involves particles oscillating in a medium; an electromagnetic wave involves oscillating electric and magnetic fields and can propagate through vacuum. In the ideal progressive mechanical-wave model, energy travels through the medium without its particles travelling along with each crest.

Transverse oscillation is perpendicular to propagation; longitudinal oscillation is parallel. A displacement graph drawn with a vertical axis does not by itself identify a transverse wave.

Recall the eight wave quantities

• Displacement: signed offset from equilibrium. Amplitude: its maximum magnitude.
• Period: time for one full repeated state at a fixed point. Frequency: cycles per second, f = 1/T.
• Phase: stage of oscillation expressed as an angle. Phase difference: the difference between two stages.
• Wavelength: distance between neighbouring points in the same phase at one instant. Wave speed: propagation rate of a phase feature.

A position snapshot gives wavelength; a fixed-point time trace gives period. The time-gradient of a displacement trace is particle velocity. To obtain wave speed, track a corresponding phase feature or use v = fλ.

Use positive separations for these phase magnitudes, then establish which point leads or lags from the propagation direction. A quarter-period delay corresponds to π/2 rad of phase; time and phase are different quantities. Equal displacement alone does not establish equal phase.

For a longitudinal displacement-position snapshot, compression depends on neighbouring particle spacing. Maximum compression occurs where the displacement gradient is most negative in the small-displacement model, not where positive displacement is largest. Revisit the separate displacement and particle-spacing representations when a graph's meaning is unclear.

State intensity conditions

Area is normal to propagation; P/A is an area average if intensity is not uniform. The amplitude ratio requires the same wave type, medium and relevant frequency conditions. Spherical inverse-square spreading additionally requires the stated point-source geometry and negligible losses, with r measured from the source centre.

In the supplied 2.0 m to 5.0 m comparison, intensity becomes 0.160 of its initial value and amplitude becomes 0.400. The power crossing each complete sphere stays the same.

Use each filter's own incident polarisation

The ideal filter selects a transverse electric-field direction. θ is the angle between the incident polarisation and the filter axis; the output is polarised along that axis. For successive filters, update both the incident intensity and its polarisation at each stage.

With plane-polarised input of 80 W/m² and axes at 45° then 90° to its original polarisation, each local angle is 45°: 80 → 40 → 20 W/m². A first ideal polariser halves unpolarised intensity; that rule does not replace Malus' law for an already plane-polarised input.

Quantities and units

Use a calibrated spatial scale, a known timebase and the correct reference point when reading data. Count full wavelength or cycle intervals, and establish the detector's calibration before treating its signal as intensity.