NZ NCEA Level 3 Physics

## Describing a wave A periodic wave repeats in both space and time. Its wavelength $\lambda$ (metres) is the distance between two neighbouring points that are in step, its frequency $f$ (hertz) is the number of complete oscillations each point makes per second, and its period is $T = \frac{1}{f}$. The speed at which the pattern moves is $$ v = f\lambda $$ where $v$ is in $\mathrm{m\,s^{-1}}$. For a given medium the speed is fixed by the medium, so a wave of higher frequency has a shorter wavelength. Sound in air at room temperature travels at about $343\,\mathrm{m\,s^{-1}}$, and light in air at very nearly $3.00\times10^{8}\,\mathrm{m\,s^{-1}}$. Two points on a wave are in phase when they are at the same stage of their oscillation, which happens when they are a whole number of wavelengths apart. They are in antiphase when one is at a crest while the other is at a trough, which happens when they are an odd number of half-wavelengths apart. The phase difference is measured as an angle, where one whole wavelength corresponds to $2\pi$ radians, so a separation of $\Delta$ along the wave gives $$ \phi = 2\pi\,\frac{\Delta}{\lambda} $$ ## The principle of superposition When two waves pass through the same point, the displacement of the medium there is the sum of the displacements each wave would produce on its own. The waves do not change each other, and once they have passed through one another each carries on as before. This is the principle of superposition, and it is the…