Wave Fundamentals and Properties

Progressive waves are the energy movers of physics - they transfer energy from one place to another without actually moving matter. Think of a Mexican wave at a football stadium: the wave travels around the stadium, but the people stay in their seats.

There are two main types: longitudinal waves (like sound) where particles vibrate parallel to the wave's direction, and transverse waves (like light) where particles vibrate perpendicular to the wave's movement. Only transverse waves can be polarised, which is why polarised sunglasses work against glare.

The key relationship you need to master is v = fλ, where v is wave speed, f is frequency, and λ is wavelength. For light, remember that speed is always 3.00 × 10⁸ m/s in a vacuum. The time period T relates to frequency as T = 1/f.

Quick Check: If you increase the frequency of a wave whilst keeping speed constant, the wavelength must decrease - they're inversely proportional!

Interference happens when two waves meet. For constructive interference (bright fringes), the path difference equals nλ. For destructive interference (dark fringes), it's $n + ½$λ. The waves must be coherent - having the same frequency, wavelength, and constant phase difference.

Stationary waves form when two identical waves travelling in opposite directions interfere. Nodes are points of zero displacement (destructive interference), whilst antinodes show maximum displacement (constructive interference). For a string fixed at both ends, the fundamental frequency is f = v/2L.

Refraction occurs when waves change speed and direction moving between different media. The critical angle $sin θc = n₂/n₁$ determines when total internal reflection happens - this is how fibre optic cables trap light signals, though pulse broadening can make signals wider and shorter over long distances.

Diffraction makes waves bend around obstacles. With diffraction gratings, constructive interference follows dsinθ = nλ, where d is the grating spacing and n is the order of diffraction.