The Principle of Superposition
Principle of Superposition - When two or more waves are simultaneously present at a single point in space, the displacement of the medium at that point is the sum of the displacements due to each individual wave.


Constructive and Destructive Interference

Standing Waves
Standing Wave - A standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions.




Nodes and Antinodes

Standing Waves on a String
Reflections

Interactions at Boundaries


Creating a Standing Wave

When can standing waves happen in a string tied at both ends?


Standing Sound Waves


Pipe Open at both Ends (open-open)

Pipe Closed at both ends (closed-closed)

Pipe Open at one end and closed at the other (open-closed)


The Interference of Waves from Two Sources
Path-Length Difference - 

Two waves will be in phase and will produce constructive interference any time their path-length difference is a whole number of wavelengths.

Two waves will be out of phase and will produce destructive interference any time their path-length difference is a whole number of wavelengths plus half a wavelength.
Interference of Spherical Waves



Beats



