Transverse and longitudinal waves, the wave quantities and the wave equation, the relationship between intensity and amplitude, and polarisation.

What this dot point is asking

CCEA wants you to distinguish transverse and longitudinal waves, define the wave quantities, use the wave equation $v = f\lambda$, relate intensity to amplitude, and explain polarisation and what it tells us about the nature of a wave. These ideas underpin the whole AS 2 module, so the definitions and the wave equation reappear in interference, refraction and medical physics.

Types of wave

Both kinds of wave transfer energy without transferring matter: the particles of the medium oscillate about fixed equilibrium positions while the disturbance moves through them. A progressive wave carries energy outward from the source, in contrast to a stationary wave, which stores energy in fixed positions.

The wave quantities

The key quantities you must define are:

• Wavelength ($\lambda$), the distance for one complete cycle, measured between two adjacent points in phase (for example crest to crest), in metres.
• Frequency ($f$), the number of complete cycles passing a point each second, in hertz ($\text{Hz}$).
• Period ($T$), the time for one complete cycle, where $T = \dfrac{1}{f}$, in seconds.
• Amplitude ($A$), the maximum displacement from the equilibrium position.
• Wave speed ($v$), the speed at which the disturbance, and hence the energy, travels.

The wave equation

Intensity and amplitude

Worked example: the wave equation and intensity

Polarisation

A plane-polarised wave oscillates in only one plane that contains the direction of travel. Ordinary (unpolarised) light contains oscillations in all planes perpendicular to its travel. A polarising filter transmits only the component of the oscillation aligned with its transmission axis, so passing light through two crossed filters (axes at $90^{\circ}$) blocks it almost completely. Rotating one filter varies the transmitted intensity between a maximum and near zero.

Polarisation has everyday uses: polarising sunglasses cut glare reflected from horizontal surfaces, and aerials are aligned to match the plane of polarisation of the broadcast signal for the strongest reception.

Examples in context

Example 1. Tuning a radio. A station transmitting at $100\ \text{MHz}$ produces waves of wavelength $\lambda = v/f = (3.0 \times 10^{8})/(1.0 \times 10^{8}) = 3.0\ \text{m}$. The aerial works best when its length matches a simple fraction of this wavelength, and it must be aligned to the plane of polarisation of the signal, showing both the wave equation and polarisation in one device.

Example 2. Earthquake waves. Seismographs detect two arrivals: fast longitudinal P-waves (which travel through liquid and solid rock) and slower transverse S-waves (which cannot pass through the liquid outer core). The fact that S-waves are blocked by liquid, while P-waves are not, is how geologists deduced that the Earth has a liquid outer core, a striking application of the transverse/longitudinal distinction.

Try this

Q1. A sound wave of frequency $440\ \text{Hz}$ travels at $340\ \text{m s}^{-1}$. Find its wavelength. [2 marks]

• Cue. $\lambda = \dfrac{v}{f} = \dfrac{340}{440} \approx 0.77\ \text{m}$.

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

• Cue. Only transverse waves can be polarised, because their oscillations are perpendicular to the direction of travel and can be restricted to one plane; longitudinal waves cannot.

Q3. The amplitude of a wave is increased by a factor of three. State the effect on its intensity. [1 mark]

• Cue. Intensity is proportional to amplitude squared, so it increases by a factor of $3^2 = 9$.