Theme C · Wave Behaviour · SL + HL · 3 hours

C.2 Wave Model

How can the wave model describe the transmission of energy through space and matter?

A wave is a disturbance that propagates, carrying energy without permanently displacing matter. The key insight is that individual particles of the medium oscillate around their equilibrium positions while the pattern of disturbance moves forward — a cork bobs up and down as a water wave passes, but it doesn't travel with the wave. This distinction between wave speed and particle speed is fundamental.

Mechanical waves (sound, water waves, seismic waves) require a medium. Electromagnetic waves do not — they are self-sustaining oscillations of electric and magnetic fields that travel at c = 3 × 10⁸ m s⁻¹ in a vacuum. The entire electromagnetic spectrum is the same phenomenon at different frequencies, from radio waves (kilometre wavelengths) to gamma rays (picometres).

A sound wave in air has a frequency of 440 Hz. If the speed of sound in air is 340 m s⁻¹, calculate the wavelength. If the same frequency is transmitted into water (speed 1500 m s⁻¹), what happens to the wavelength, and why does this matter for refraction?

Key equations

Wave speed: v = fλ = λ/T

What students must understand

Transverse waves: displacement perpendicular to propagation (e.g. EM waves, waves on a string)
Longitudinal waves: displacement parallel to propagation (e.g. sound, P-waves)
Wavelength λ, frequency f, period T, and wave speed v; the relationship v = fλ
Nature of sound: longitudinal pressure wave in a medium; compressions and rarefactions
Nature of EM waves: oscillating E and B fields, perpendicular to each other and to propagation; no medium needed
Key difference: mechanical waves need a medium; EM waves travel in a vacuum
The EM spectrum: approximate wavelengths of radio, microwave, infrared, visible, UV, X-ray, gamma (from data booklet)