C.2 Wave model

Follow one particle, not the drawn shape

At a fixed position, a medium particle oscillates with time about equilibrium. In a position snapshot, different particles have different displacements at the same instant. The travelling pattern and energy move through the medium; the particles do not travel with the pattern.

Classification rule

Compare the particle or field oscillation direction with the propagation direction. A sinusoidal-looking graph alone does not determine whether a wave is transverse or longitudinal.

Define the quantities

Wavelength $\lambda$ is the shortest distance between points in phase. Frequency $f$ is cycles per second, period $T$ is the time for one cycle, and amplitude is maximum displacement from equilibrium. Wave speed $v$ is the speed at which the disturbance and energy propagate.

Connect time and space

For a travelling wave, $v=f\lambda=\lambda/T$. Use a spatial wavelength measured in metres and a temporal frequency measured in hertz; the result is in metres per second.

Read the same ideas in both wave types

For transverse waves, wavelength can be measured crest-to-crest or trough-to-trough. For longitudinal waves, measure compression-to-compression or rarefaction-to-rarefaction. In both cases the points are in phase.

Common trap

Do not use the distance from a crest to the next trough as one wavelength; that is half a wavelength. Do not confuse the speed of the medium particles with the propagation speed $v$.

Sound needs a mechanical medium

Sound is produced by a vibrating source and travels through matter as a mechanical wave. In air it is longitudinal: air molecules oscillate back and forth parallel to the direction in which the disturbance and energy propagate.

Compressions and rarefactions

A compression is a region of higher particle density and pressure; a rarefaction is a region of lower density and pressure. One wavelength is the distance between neighbouring compressions or neighbouring rarefactions.

Exam-language calibration from local practice question 2

A complete description connects all four ideas: longitudinal particle motion, propagation through air, alternating compressions/rarefactions, and energy transfer away from the source.

Boundary

The air molecules oscillate locally; they are not carried from loudspeaker to listener. Sound cannot propagate through a vacuum because there are no particles to sustain the mechanical disturbance.

Oscillating fields

An electromagnetic wave consists of oscillating electric and magnetic fields. The two fields are perpendicular to each other and both are perpendicular to the direction of propagation and energy transfer, so the wave is transverse.

No material medium is required

Electromagnetic fields can propagate through a vacuum. Every electromagnetic wave travels in vacuum at $c=3.00\times10^8\,\mathrm{m\,s^{-1}}$, with $c=f\lambda$.

One spectrum, approximate regions

Radio, microwave, infrared, visible, ultraviolet, X-ray and gamma radiation are all electromagnetic waves. Use the approximate wavelength orders of magnitude supplied in the Physics data booklet; the named regions do not have perfectly sharp physical boundaries.

Common trap

Different spectrum regions do not have different vacuum speeds. They differ in frequency and wavelength while satisfying the same value of $c$.

Energy moves without net medium displacement

In a travelling mechanical wave, particles oscillate about equilibrium and pass the disturbance onward, so energy moves even though the medium has no resultant displacement after a complete cycle. In an electromagnetic wave, oscillating fields carry energy through space.

Use the same relationship carefully

Both models obey $v=f\lambda$, but $v$ is set by the relevant medium or, for electromagnetic waves in vacuum, by $c$. The source frequency links the spatial pattern to how rapidly the local oscillation repeats.

Common trap

“Transfers energy” does not mean matter must travel from source to receiver. It also does not mean mechanical and electromagnetic waves have the same physical oscillator.