Waves - Physics

Simple Harmonic Motion (SHM)

Oscillatory motion where the acceleration of an object is directly proportional to its displacement from equilibrium and directed toward that equilibrium position (a = -ω²x).

Phase Difference

The fraction of a cycle or wave period by which two vibrating points or waves differ in time or position, measured in radians or degrees.

Path Difference

The difference in physical distance traveled by two coherent waves from their respective sources to a given point of interference.

Coherent Sources

Two or more wave sources that emit waves with the same frequency, wavelength, and a constant phase difference.

Superposition Principle

When two or more overlapping waves meet at a point, the resultant displacement is the vector sum of the individual displacements.

Constructive Interference

The superposition of two in-phase waves where crest meets crest, resulting in a wave with maximum amplitude (path difference = nλ).

Destructive Interference

The superposition of two out-of-phase waves where crest meets trough, resulting in a wave with minimum or zero amplitude (path difference = (n - ½)λ).

Standing Wave

A wave pattern formed by the superposition of two identical waves traveling in opposite directions, characterized by fixed nodes and antinodes.

Node

A point along a standing wave where maximum destructive interference occurs, resulting in zero amplitude displacement.

Antinode

A point along a standing wave where maximum constructive interference occurs, resulting in maximum amplitude displacement.

Fundamental Frequency

The lowest resonant frequency (f₁) at which a system forms a standing wave pattern.

Harmonic

An integer multiple of the fundamental frequency produced in a standing wave system.

Overtone

Any resonant frequency higher than the fundamental frequency in an oscillating system.

Diffraction

The spreading out of waves as they pass through a narrow slit or around the edge of an obstacle.

Two-Slit Interference

Interference pattern produced when light passes through two slits separated by distance d, given by d sin(θ) = nλ or nλ = dx/L.

Diffraction Grating

A plate containing thousands of closely spaced parallel lines that produces sharp, widely spaced interference maxima given by d sin(θ) = nλ.

Central Maximum

The brightest central fringe (n = 0) in an interference or diffraction pattern where the path difference between light paths is zero.

Beats

Periodic variations in loudness or amplitude produced when two waves of slightly different frequencies interfere (f_beat = |f₁ - f₂|).

Beat Frequency

The rate at which the sound intensity rises and falls, equal to the absolute difference between the two frequencies (f_beat = |f₁ - f₂|).

Doppler Effect

The apparent change in frequency of a wave caused by relative motion between the wave source and the observer (f' = f v_w / (v_w ± v_s)).

Red Shift

The shift of spectral lines toward longer wavelengths (lower frequencies) when a light source moves away from the observer.

Blue Shift

The shift of spectral lines toward shorter wavelengths (higher frequencies) when a light source moves toward the observer.

Angular Frequency (ω)

The rate of change of phase angle per unit time, measured in radians per second (ω = 2πf = 2π/T).

Natural Frequency

The unique frequency at which an object or system naturally tends to vibrate when disturbed without external driving forces.

Resonance

The phenomenon occurring when a driving frequency matches a system's natural frequency, producing a dramatic increase in vibration amplitude.