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Superposition summary

Principle of superposition: sum over amplitudes of different waves

  • Destructive interference results in a lower amplitude and constructive interference in a higher amplitude.

Diffraction: bending of a wave around an obstacle.

Young's double-slit experiment: bright and dark fringes of interference.

$$$\lambda=\frac{ax}{D}$$$

$$a$$ is the slit width; $$x$$ is the distance between fringes; $$D$$ is the distance between the double-slit and the screen; $$\lambda=$$ wavelength.

Diffraction grating: fringes of interferences from a periodic material with an order that increases from the central maximum: $$$d\sin\theta=n\lambda$$$

$$n=$$order of the maximum; $$d=$$distance between the grating lines; $$\theta=$$angle between the location of a maximum and the midpoint of the grating.

Stationary waves possess nodes (fixed points) and anti-nodes (maximally moving points). A reflected wave is always anti-phase

Waves on strings and in pipes decompose into fundamental and higher harmonic modes:

  • $$L_{\text{string}}=\frac{n\lambda}{2}$$, $$n=$$the number of antinodes.
  • $$L_{\text{closed}}=\frac{n\lambda}{4}$$, $$n=$$odd integer.
  • $$L_{\text{open}}=\frac{n\lambda}{2}$$, $$n=$$any integer.