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 doubleslit 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 doubleslit 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 antinodes (maximally moving points). A reflected wave is always antiphase
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.