Unit 14 · Waves, Sound, and Physical Optics

Wave pulse vs. wave ● (core concept) — A wave pulse is a single disturbance that transfers energy without transferring matter. A wave is a continuous, periodic disturbance with a well-defined wavelength and frequency.

Mechanical vs. electromagnetic waves ● (core concept) — Mechanical waves (sound, string waves) require a medium to propagate; electromagnetic waves do not. All EM waves travel at c = 3.00×10⁸ m/s in vacuum.

Wave speed in a medium ● (core concept) — A wave's speed is set by the wave type and the medium's properties, not by the source. For a string, v = √(F_T/(m/ℓ)): higher tension or lower linear mass density means faster waves. Sound speed rises with the medium's temperature.

Transverse vs. longitudinal wave ● (core concept) — In a transverse wave the disturbance is perpendicular to the propagation direction; in a longitudinal wave it is parallel. Sound is a mechanical longitudinal wave whose high- and low-pressure regions are compressions and rarefactions.

Amplitude (wave) ● (core concept) — The maximum displacement of a wave from equilibrium (for a sound wave, the maximum pressure deviation). Louder sounds have larger amplitude, and a wave's energy increases with increasing amplitude.

Compression and rarefaction ● (core concept) — The high-pressure and low-pressure regions of a longitudinal sound wave. Air molecules oscillate back and forth along the propagation direction, bunching into compressions and spreading into rarefactions.

Period and frequency ● (core concept) — The period T is the time for one complete oscillation; the frequency f is the repetition rate, with T = 1/f. Amplitude is independent of period and frequency.

Wavelength ● (core concept) — λ: the distance between successive corresponding points on a wave (peak to peak, trough to trough). Related to speed and frequency by v = fλ.

Frequency, pitch, and energy ● (core concept) — A sound wave's frequency determines its pitch. A wave's energy increases with increasing frequency (and, separately, with amplitude).

Boundary behavior: reflection and transmission ● (core concept) — A wave hitting a boundary between media is partly reflected and partly transmitted. The reflected pulse inverts if the new medium is slower (denser for a string) and does not invert if the new medium is faster. The frequency never changes across a boundary.

Polarization ● (core concept) — The restriction of a transverse wave's oscillations to a single plane (e.g., by reflection, refraction, or passing through a polarizer). Longitudinal waves cannot be polarized. Polarizing a wave reduces its intensity.

Wave intensity ● (core concept) — The power transferred per unit area by a wave.

Electromagnetic wave (structure) ● (core concept) — Oscillating electric and magnetic fields that are mutually perpendicular and both perpendicular to the propagation direction — hence a transverse wave, commonly modeled as a plane wave with planar wavefronts.

Electromagnetic spectrum (order) ● (core concept) — In order of decreasing wavelength: radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays. Students must know the order, not exact wavelength ranges.

Visible light colors (order) ● (core concept) — In order of decreasing wavelength: red, orange, yellow, green, blue, violet.

Wavefront ● (core concept) — A surface joining points of a wave that are in phase (e.g., all the wave crests). Light rays are perpendicular to wavefronts; a plane wave has planar wavefronts.

Plane wave ● (core concept) — The common model of an electromagnetic wave as having planar wavefronts with the electric and magnetic fields oscillating perpendicular to each other and to the propagation direction.

Doppler effect ● (core concept) — The shift between a wave source's rest frequency and the observed frequency due to relative motion between source and observer. Approaching motion raises the observed frequency; receding motion lowers it; larger relative speed means a larger shift. Only qualitative treatment is required.

Superposition ● (core concept) — When two or more waves overlap, they pass through each other and the resulting displacement is the sum of the individual displacements at each point.

Constructive vs. destructive interference ● (core concept) — Constructive interference: overlapping displacements in the same direction reinforce. Destructive interference: overlapping displacements in opposite directions cancel.

Beats ● (core concept) — Periodic amplitude variation from adding two waves of slightly different frequency. The beat frequency is the difference: f_beat = |f₁ − f₂|.

Standing wave ● (core concept) — A wave pattern formed by two identical waves confined to a region and traveling in opposite directions. It has nodes (points of always-zero amplitude) and antinodes (points of maximum amplitude).

Harmonics ● (core concept) — The allowed standing-wave wavelengths set by a region's size and boundary conditions. The longest wavelength is the fundamental (first harmonic); higher harmonics are shorter. A pipe/string fixed or closed at both ends fits L = nλ/2 (n = 1, 2, 3, …); a pipe closed at one end fits L = nλ/4 with only odd n.

Node (standing wave) ● (core concept) — A point on a standing wave that always has zero amplitude — the wave never moves there. Adjacent nodes are half a wavelength apart.

Antinode (standing wave) ● (core concept) — A point on a standing wave with maximum oscillation amplitude, located halfway between two adjacent nodes.

Diffraction ● (core concept) — The spreading of a wave around an obstacle's edge or through an opening — most pronounced when the opening is comparable to the wavelength. Multiple wavefronts through one opening produce interference patterns.

Single-slit diffraction pattern ● (core concept) — Monochromatic light through a narrow slit of width a produces bright and dark bands from interfering wavefronts. The path-length difference is Δ = a·sinθ; dark minima (destructive) occur where Δ = mλ (m = ±1, ±2, …), located at y_min ≈ mλL/a for small angles (L = slit-to-screen distance).

Monochromatic light ● (core concept) — Light of a single wavelength (single color), as produced by a laser. Single-slit, double-slit, and grating analyses assume monochromatic light so each wavelength's pattern can be treated separately.

Double-slit interference ● (core concept) — Two slits a distance d apart produce uniformly spaced bright maxima where the path difference is Δ = d·sinθ = mλ (m = 0, ±1, …), at positions y_max ≈ mλL/d for small angles. The interference fringes sit inside the broader single-slit diffraction envelope. Young's double-slit experiment established light's wave nature.

Diffraction grating ● (core concept) — Many evenly spaced parallel slits whose superimposed diffraction patterns give sharp bright maxima at d·sinθ = mλ. White light through a grating disperses into rainbows with red (longest wavelength) farthest from the central white maximum.

Interference order ● (core concept) — The integer m = 0, ±1, ±2, … labeling bright maxima (constructive) or dark minima (destructive) in two-slit, grating, and single-slit patterns, via path-difference conditions such as d·sinθ = mλ.

Thin-film interference ● (core concept) — Interference between light reflected from a film's front surface and light reflected from its back surface, significant when the film thickness is comparable to the wavelength. Whether the interference is constructive or destructive depends on film thickness, wavelength, incidence angle, and phase shifts. Quantitative analysis is limited to normal incidence.

Phase change on reflection ● (core concept) — A light ray reflected from a medium with a HIGHER index of refraction than the one it travels in undergoes a 180° phase shift; reflection from a LOWER index gives no phase shift. Refraction (transmission) never changes the phase.

Antireflection coating ● (core concept) — A thin film that cancels reflected light by destructive interference: its thickness is one-quarter of the light's wavelength in the coating, and its index lies between air's and the surface's. Soap-bubble and oil-film colors arise the same way, from thickness variations across the film.