Wave Properties

In a $\textbf{transverse}$ wave the particles of the medium oscillate perpendicular to the direction of energy transfer — waves on a string, ripples on water, and all electromagnetic waves.

In a $\textbf{longitudinal}$ wave the oscillation is parallel to the direction of travel, producing regions of $\textbf{compression}$ and $\textbf{rarefaction}$ — sound in air, and the P-waves of an earthquake.

Only transverse waves can be $\textbf{polarised}$, since a longitudinal oscillation has only one possible direction. That difference is how polarisation proves light is transverse.

$\textbf{Amplitude}$ $A$ is the maximum displacement from equilibrium. $\textbf{Wavelength}$ $\lambda$ is the distance between two consecutive points in phase, such as crest to crest. $\textbf{Period}$ $T$ is the time for one complete oscillation, and $\textbf{frequency}$ $f$ is the number of oscillations per second, so $f = 1/T$.

In one period the wave advances one wavelength, so its speed is $v = \lambda/T = f\lambda$ — the wave equation.

The speed is set by the medium, not the source. When a wave crosses into a new medium its frequency stays fixed (it is set by the source) and the wavelength changes to match the new speed.

$\textbf{Phase}$ describes the position of a point within its cycle. One whole cycle is $360^{\circ}$ or $2\pi$ radians.

Two points one wavelength apart are $\textbf{in phase}$ (difference $2\pi$, equivalent to zero). Two points half a wavelength apart are in $\textbf{antiphase}$ — difference $\pi$ — moving in opposite directions at every instant.

For points separated by a distance $x$ along the wave, the phase difference is the fraction of a wavelength, times $2\pi$.

$\textbf{Intensity}$ is power per unit area, $I = P/A$, in $\mathrm{W\,m^{-2}}$. For a wave, intensity is proportional to amplitude squared — doubling the amplitude quadruples the energy delivered.

For a point source radiating equally in all directions, the power spreads over a sphere of area $4\pi r^{2}$, giving the inverse-square law.

An oscilloscope displays a signal’s displacement against time. Frequency is found from the period read off the screen using the time-base setting, and amplitude from the vertical divisions using the volts-per-division setting.