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Wave motion summary

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

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.