Concepts of Displacement, Coherence, Path Difference, Phase Difference and Superposition

Displacement

Displacement, in the context of waves, is the distance moved by a point on the wave in a particular direction from its equilibrium position.
It is a vector quantity as it involves both magnitude and direction.
For a wave oscillating up and down, a displacement above the equilibrium is often considered as positive and one below as negative.
For waves like light or sound, the directions of displacement of particles are perpendicular and parallel to the direction of wave propagation respectively.

Coherence

Coherence refers to the property of waves that enables them to maintain a constant phase difference and produce an interference pattern.
It is a crucial concept for understanding phenomena like diffraction and interference.
Two sources of light, e.g. two lasers, are said to be coherent if they emit waves with a constant phase difference.
Coherent waves are often produced from a single source using techniques like splitting a single light beam.

Path Difference

Path difference relates to the difference in the lengths of the paths taken by two waves from their respective sources to a common point.
It is generally measured in terms of the wavelength of the waves.
Path difference influences the type of interference produced when two waves meet — if the path difference is an integer multiple of the wavelength, constructive interference occurs; if it is an odd half multiple of the wavelength, destructive interference occurs.

Phase Difference

Phase difference is the difference in phase between two points on the same wave or between corresponding points on two similar waveforms.
It is usually measured in degrees or radians. One full wave cycle corresponds to 360 degrees or 2π radians.
Phase differences play a key role in phenomena like interference and superposition, determining whether constructive or destructive interference occurs when two waves meet.

Superposition

Superposition is a fundamental concept in wave mechanics stating that, when two or more waves meet, the resultant wave is the vector sum of the individual waves.
This principle underlies the interference of waves and can lead to constructive or destructive interference.
Constructive superposition occurs when waves meet in phase and their amplitudes add together; destructive superposition occurs when waves meet out of phase and their amplitudes subtract from each other.
The waveforms resulting from superposition can provide significant information about the waves involved, including their amplitudes, frequencies, and phase relationships.

Understanding these concepts helps in understanding wave behaviour and the phenomena related to it, such as interference, diffraction, and resonance. They form an integral part of learning about wave mechanics.