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# Wave motion summary

## Summary of wave properties

Propagation

Progressive wave: travels through space, net transfer of energy.

Stationary wave: does not travel, no net transfer of energy.

Direction of oscillation

Transverse wave (e.g. light): direction of oscillation perpendicular to the direction of motion of the wave (presents crests and troughs).

Longitudinal wave (e.g. sound): direction of oscillation parallel to the direction of motion of the wave (compression-rarefactions).

Quantities:

Wavelength $(\lambda)$: distance travelled by the wave in one period.

Speed: $\displaystyle{v=f\lambda=\frac{\lambda}{T}}$

## Summary of concepts in wave intensity and polarisation

Phase: $\displaystyle{\phi=\frac{2\pi d}{\lambda}}$

Phase difference between two particles in a wave: $\displaystyle{\Delta\phi=\frac{2\pi\vert d_{2}-d_{1}\vert}{\lambda}}$

• Particles in phase: same displacement from an equilibrium position $\Delta\phi = 2\pi n$ with $n$ an integer.
• Particles out of phase:different phases
• Particles in anti-phase: $\Delta\phi = \pi n$

Intensity $(I)$: $$I=\frac{P}{A} \quad \text{and} \quad I\propto x_{0}^{2}$$ $P=$ energy flux/power imparted by the wave; $A=$ area normal to the direction of wave motion; $x_{0}=$ amplitude of the wave.

Uniformly radiating point source: radiates energy in all directions equally. $$I=\frac{P_{\text{S}}}{4\pi r^{2}}$$ $r=$ distance from the source.

Polarised wave (transverse wave only): oscillations aligned into a particular pattern. In contrast with an unpolarised wave.

Through a polariser:

• Amplitude: $A=A_{0}\cos\theta$
• Intensity: $I=I_{0}\cos^{2}\theta$

Axis angled at $\theta$ to the wave oscillations.