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# Superposition summary

## Summary of superposition

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.