Waves

• Displacement, amplitude, phase difference, period, frequency, wavelength and speed.
• A CRO measures period from the time-base and amplitude from the y-gain.
• Wave equation v = fλ; intensity = power/area and intensity ∝ amplitude².
• Transverse: oscillations perpendicular to energy transfer. Longitudinal: oscillations parallel to it.
• Doppler effect for a moving source: f_o = f_sv/(v ± v_s).
• All electromagnetic waves are transverse and travel at c in free space; visible light is 400–700 nm.
• Only transverse waves can be polarised; Malus's law I = I₀ cos² θ.

Describing a wave and the energy it carries

Wave motion can be seen in ropes, slinky springs and ripple tanks: each particle oscillates about its equilibrium position while the wave pattern, and the energy, move along.

• Displacement: distance of a point from its equilibrium position.
• Amplitude: maximum displacement.
• Period T: time for one complete oscillation. Frequency f = 1/T, oscillations per unit time.
• Wavelength λ: distance between adjacent points oscillating in phase (e.g. crest to crest).
• Phase difference: how far one oscillation is ahead of another, in degrees or radians; points Δx apart differ by 360° × Δx/λ.

Deriving v = fλ: in one period T the wave moves forward one wavelength λ, so v = λ/T = fλ.

On a CRO the time-base (s per division) converts horizontal divisions into time; the y-gain (V per division) converts vertical divisions into voltage.

Intensity is power per unit area perpendicular to the direction of travel, and for a progressive wave it is proportional to amplitude squared.

Two ways to oscillate

In a transverse wave the particles oscillate perpendicular to the direction of energy transfer (waves on a string, water ripples, all electromagnetic waves). In a longitudinal wave they oscillate parallel to the direction of energy transfer, creating compressions and rarefactions (sound, a slinky pushed and pulled along its length).

displacement–distance displacement–time

A moving source