Transverse and longitudinal waves, amplitude, wavelength, frequency, period and phase, the wave equation, and polarisation.

What this dot point is asking

WJEC wants you to distinguish transverse from longitudinal waves, define the wave quantities and phase, use the wave equation, and explain polarisation as evidence that a wave is transverse. These definitions and the wave equation are foundational, reappearing in every later wave topic from interference to standing waves, and polarisation is a favourite short-answer question.

The answer

Transverse and longitudinal waves

In both cases the wave transfers energy without transferring matter: the medium oscillates about a fixed point but does not travel with the wave.

Wave quantities and the wave equation

Amplitude is the maximum displacement from equilibrium. Wavelength $\lambda$ is the distance between two adjacent points in phase. Frequency $f$ is the number of cycles per second and period $T$ the time for one cycle, with $f = \dfrac{1}{T}$. Phase difference describes how far through a cycle one point is relative to another, usually measured in radians, where a full cycle is $2\pi$.

The wave equation follows from the definitions: in one period $T$ the wave advances exactly one wavelength $\lambda$, so $v = \lambda / T = f\lambda$.

Polarisation

That light can be polarised (for example by a Polaroid filter) is direct evidence that light is a transverse wave.

Examples in context

Example 1. Polarised sunglasses

Light reflected off a wet road or water surface is partly horizontally polarised. Polaroid sunglasses are oriented to block this horizontal component, cutting glare while still letting through vertically polarised light from the rest of the scene. This everyday product is a direct application of the transverse nature of light.

Example 2. Seismic waves locating an earthquake

An earthquake produces fast longitudinal P-waves and slower transverse S-waves. Because S-waves are transverse, they cannot pass through the liquid outer core, and the resulting shadow zone helped reveal the Earth's layered structure. The time gap between the P and S arrivals, combined with the wave equation, lets seismologists pinpoint the distance to the epicentre.

Example 3. Tuning a radio

A radio receiver selects one station by matching its circuit to the frequency of the incoming electromagnetic wave. Since $v = f\lambda$ and all such waves travel at $c$, choosing a frequency is the same as choosing a wavelength. The aerial must also be aligned with the plane of polarisation of the transmitted wave to pick up the strongest signal, which is why car aerials are angled the way they are.

Try this

Q1. A wave has frequency $50\,\text{Hz}$ and wavelength $6.0\,\text{m}$. Find its speed. [2 marks]

• Cue. $v = f\lambda = 50\times6.0 = 300\,\text{m s}^{-1}$.

Q2. Explain how polarisation shows that light is a transverse wave. [2 marks]

• Cue. Only transverse waves can be polarised; light can be polarised, so it must be transverse.