Longitudinal and transverse waves and polarisationAQA A-Level Physics: Revision notes

Waves are classified by the direction in which the particles (or fields) oscillate relative to the direction of energy transfer, which is the direction the wave travels.

• In a transverse wave the oscillations are perpendicular to the direction of energy transfer. Examples: waves on a string, ripples on water, and all electromagnetic waves (where it is electric and magnetic fields that oscillate).
• In a longitudinal wave the oscillations are parallel to the direction of energy transfer. Particles are pushed together (compressions) and pulled apart (rarefactions). Examples: sound in air, and compression waves on a spring.

In both cases the particles only oscillate about fixed positions; energy, not matter, is transferred.

Electromagnetic waves are transverse waves of oscillating electric and magnetic fields at right angles to each other and to the direction of travel. The electromagnetic spectrum includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays.

They need no medium and all travel at the same speed in a vacuum, $c = 3.00\times10^{8}\ \text{m s}^{-1}$, whatever their frequency or wavelength. Because $c = f\lambda$, the higher the frequency, the shorter the wavelength.

Worked example. A radio signal sent to a satellite 3.6 × 10⁷ m away takes $t = 3.6\times10^{7}/3.00\times10^{8} = 0.12$ s. An infrared pulse sent at the same instant arrives at the same time.

An unpolarised transverse wave has oscillations in all directions perpendicular to its direction of travel. Plane polarised means the oscillations are restricted to one plane (the electric field, for light).

A polarising filter such as Polaroid has a transmission axis. It transmits the oscillations along that axis and absorbs those perpendicular to it. Unpolarised light that passes through a filter is plane polarised, and its intensity is reduced.

With two filters, rotating the second (the analyser) while the first is fixed changes the transmitted intensity from a maximum, when the axes are parallel, to zero when they are at 90° (crossed). This occurs twice per full rotation. (You are not expected to use Malus's law.)

Only waves with oscillations perpendicular to the direction of travel can be restricted to one plane. The fact that light can be polarised, and that crossed polarisers block it completely, is therefore evidence that light is a transverse wave. Sound is longitudinal, so its oscillations are already along one line (the direction of travel) and no filter can select a plane. Rotating a filter in the path of sound changes nothing.

• Polarising sunglasses use Polaroid with the transmission axis vertical. Light reflected from horizontal surfaces such as water or roads is partly polarised horizontally, so it is blocked and glare is reduced. Tilting the head by 90° lets the glare back through.
• Cameras use a polarising filter to cut reflections from glass or water.
• Aerials: a rod aerial transmits plane polarised radio waves with the electric field parallel to the rod. A receiving rod aerial gives the strongest signal when parallel to that field, and almost none when at 90° to it, so aerials must be aligned in the same plane of polarisation for good reception.
• Microwaves: a metal grille polarises or detects microwaves in the same way.