Revise Progressive waves for Cambridge 9702 (7.1)

A progressive wave is essentially a disturbance that travels through a medium or even a vacuum, carrying energy along with it. Crucially, while the energy progresses, the individual particles of the medium merely oscillate around their fixed equilibrium positions. They don't travel along with the wave itself.

To describe waves precisely, we use several fundamental terms. These quantities are interconnected and allow us to mathematically model wave behaviour. They can be determined from graphical representations of the wave.

The Wave Equation: $v = f\lambda$

We can visualize waves using two types of graphs. A displacement-distance graph is a snapshot of the wave at a single moment in time, showing the displacement of all particles along the wave's path. A displacement-time graph shows the oscillation of a single particle over a period of time.

The phase of a point on a wave describes its position and direction of motion within its oscillation cycle. The phase difference between two points compares their positions in the cycle. Points that are moving together are 'in phase' (phase difference of 0 or $2\pi$ radians), while points moving in exact opposition are 'in antiphase' (phase difference of $\pi$ radians).

Phase difference $\phi$ (in radians) for two points separated by a distance $x$ is given by: $\phi = \frac{x}{\lambda} \times 2\pi$

The intensity of a wave ($I$) is defined as the power ($P$) it transfers per unit area ($A$) perpendicular to the direction of energy transfer. A key relationship is that intensity is directly proportional to the square of the wave's amplitude.

Intensity: $I = \frac{P}{A}$ and $I \propto A^2$

Not all waves are the same! The way the particles of a medium oscillate relative to the wave's direction of energy transfer categorises them into two main types: transverse and longitudinal waves. This distinction is crucial for understanding their unique properties.

Polarisation is a unique property of transverse waves. It involves restricting the oscillations of the wave to a single plane. This phenomenon provides definitive evidence that waves like light are transverse, as longitudinal waves, with oscillations parallel to the direction of travel, cannot be polarised.

Malus' Law (for transmitted intensity through a polariser): $I = I_0\cos^2\theta$

Ever noticed how the pitch of an ambulance siren changes as it approaches and then moves away? That's the Doppler effect in action! It's the apparent shift in a wave's frequency and wavelength due to the relative motion between the source of the wave and the observer.