A-level Physics/Wave properties/Superposition

When two waves are superimposed the displacement of the resultant wave is equal to the algebraic sum of the individual displacements.

Diffraction and interference

Diffraction is the spreading out of waves as they pass through a narrow gap or obstacle. When light diffracts through two slits, the relationship connecting the separation of the light sources (i.e., the separation of the slits), a, the separation of the fringes of the interference pattern, x, the wavelength of the light and the distance of the screen from the sources, D is as follows:

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

Superposition

At a point where two or more waves meet, the instantaneous displacement is the vector sum of the individual displacement due to each wave at that point.

Coherence

Two waves are said to be coherent with each other if the path difference between them stays constant from the source up to the detection.they may or may not have same wavelength, frequencies and amplitudes.

Monochromatic

Waves of a single wavelength or frequency are monochromatic.

Path Difference

Path difference = $n\,\lambda$ for constructive waves.

Path difference = $(n\ +{\frac {1}{2}})\lambda$ for destructive waves.

(where n is an integer).

Formation of a stationary wave

It forms due to the superposition of wave travelling in 1 direction with a wave of equal amplitude and wavelength travelling in the opposite direction.

Stationary waves on a string occur when $1\ =n\,{\frac {\lambda }{2}}$