Glossary

Terms used in this book.

A reference list of the technical vocabulary used in What is sound?. Inline occurrences of these terms in the lessons are auto-tooltipped (dotted underline) so you can hover for a quick definition; for a fuller treatment with context, return here.

212 terms from this book.

A

absorption coefficient: The fraction of incident sound energy absorbed by a surface (α = 1 − |R|²). Ranges from 0 (perfect reflection) to 1 (perfect absorption).
acoustic energy density: Energy per unit volume in a sound field: e = p²/(2ρc²) + ½ρv². Sum of potential (pressure) and kinetic (velocity) energy densities.
acoustic impedance: The ratio of acoustic pressure to particle velocity in a propagating wave (Z = p/v). For a plane wave in a medium of density ρ and wave speed c, Z = ρc.
acoustic intensity: Time-averaged energy flux: ⟨I⟩ = ⟨p′v′⟩ = P₀²/(2ρc) for a plane wave, in W/m².
acoustic streaming: Steady mean flow driven by absorption of acoustic momentum in a viscous medium.
adiabatic: A process in which no heat is exchanged with the surroundings. Sound propagation in air is adiabatic because compressions/rarefactions happen too fast for heat conduction.
aliasing: The artefact that occurs when a signal is sampled below the Nyquist rate: high frequencies masquerade as lower ones, folding back into the baseband.
amplitude: The magnitude of a wave's departure from equilibrium. For sound, the size of the pressure fluctuation.
angular frequency: Rate of phase advance in radians per second: ω = 2πf.
anti-aliasing filter: An analog low-pass filter applied before sampling to remove content above the Nyquist frequency.
antinode: A point in a standing wave where the amplitude is maximum. Located midway between nodes; the sites of maximum displacement or pressure variation.
auditory nerve: The ~30,000-fibre bundle carrying spike-train information from the cochlea to the cochlear nucleus in the brainstem.

B

band-limited: A signal containing no frequency content above some maximum frequency B. Such signals can be perfectly reconstructed from samples at rate ≥ 2B.
basilar membrane: The membrane separating scala media from scala tympani. Its position-dependent stiffness gives different places different natural frequencies.
beats: Slow amplitude modulation heard when two tones of nearly equal frequency are superposed; beat rate = |f₁−f₂|.
Bernoulli equation: For steady, inviscid, incompressible flow along a streamline: P + ½ρv² + ρgz = const. Energy conservation per unit volume.
Bessel function: Solutions to Bessel's differential equation, arising in problems with cylindrical symmetry. J_n(x) are finite at the origin; Y_n(x) diverge there.
Bode plot: A log-frequency plot of transfer-function magnitude and phase; the standard visualisation of filter response.
boundary layer: The thin region near a solid surface where viscous effects are significant and velocity transitions from zero (no-slip) to the free-stream value.
boundary-value problem: A differential equation with conditions specified at two or more spatial points, rather than at an initial time.
Brownian motion: The random motion of a particle suspended in a fluid, driven by molecular collisions. Mathematically: a continuous-time stochastic process with Gaussian independent increments.
bubble cloud: Ensemble of interacting cavitation bubbles whose collective dynamics differ from isolated single-bubble behavior.
bulk modulus: The resistance of a material to uniform compression: K = −V(dp/dV). Higher K means stiffer material and faster sound propagation.
Burgers equation: Nonlinear PDE combining propagation with diffusion: ∂v/∂t + βv ∂v/∂x = ν ∂²v/∂x². Models shock formation.

C

characteristic curve: Curve in (x,t) space along which information propagates; for the wave equation, lines x ± ct = const.
characteristic frequency: The frequency at which a given place on the basilar membrane (or auditory-nerve fibre) responds most strongly.
cochlea: The spiral, fluid-filled organ of the inner ear that performs frequency analysis on incoming sound and transduces it into neural signals.
cochlear amplifier: The active feedback process in the cochlea, driven by outer-hair-cell electromotility, that sharpens basilar-membrane tuning beyond passive mechanics.
compressibility: The fractional volume change per unit applied pressure: κ = −(1/V)(dV/dp). The reciprocal of the bulk modulus. Air's high compressibility is why sound exists in it.
constructive interference: When two waves combine in phase, doubling amplitude. Aligned phasors sum to twice their individual magnitude.
continuity equation: The local conservation law: ∂ρ/∂t + ∇·(ρv) = 0. Any density change equals the negative divergence of the flux.
control volume: A fixed region in space through which fluid flows; used to derive conservation laws in integral form.
convective derivative: D/Dt = ∂/∂t + U·∇; rate of change following a fluid element moving at velocity U.
convolution: A mathematical operation combining two signals: the output at time t is the weighted sum of one signal across all times, weighted by the other shifted to t.
convolution theorem: Convolution in the time domain corresponds to multiplication in the frequency domain: F{f*g} = F{f}·F{g}. The computational basis for fast filtering via FFT.
critical angle: The angle of incidence beyond which total internal reflection occurs: θ_c = arcsin(c₁/c₂). Only exists when c₂ > c₁.
critically damped: A damped oscillator with γ = ω₀: returns to equilibrium as fast as possible without oscillating. The design target for many engineered systems.
CROS: Contralateral Routing of Signal. A hearing-aid configuration for unilateral deafness: a microphone on the dead ear transmits wirelessly to a receiver on the better ear.

D

d'Alembert's solution: The general solution to the 1-D wave equation: u(x,t) = f(x−ct) + g(x+ct). Any disturbance splits into two pulses traveling in opposite directions.
damped natural frequency: The oscillation frequency of a damped system: ω_d = √(ω₀² − γ²), slightly lower than the undamped natural frequency.
damped oscillation: Oscillation with energy loss (friction, viscosity, radiation). Amplitude decays exponentially; the system eventually returns to equilibrium.
damping rate: The coefficient γ controlling exponential energy loss in a damped oscillator. Sets the decay envelope e^{−γt}.
dB SPL: Decibels Sound Pressure Level. Referenced to 20 μPa (the threshold of hearing at 1 kHz). An absolute physical measure, unlike dB HL.
decibel: A logarithmic unit of ratio: 20·log10(amplitude ratio) or 10·log10(power ratio). Used for sound pressure level (SPL) and hearing level (HL).
destructive interference: When two waves combine with opposite phase, reducing or cancelling amplitude. Phasors 180° apart sum to zero.
differential equation: An equation relating an unknown function to its derivatives. ODEs involve one variable; PDEs involve several.
diffraction: The bending of waves around obstacles or through apertures. Significant when the obstacle size is comparable to or smaller than the wavelength.
diffusion coefficient: D, in Fick's law J = −D∇c. Measures how fast a species spreads. For a sphere in fluid: D = k_BT/(6πμa) (Stokes-Einstein).
diffusion equation: The parabolic PDE ∂u/∂t = D∇²u describing how a concentration or temperature field spreads out over time. Solutions are Gaussian spreading profiles.
diffusivity: The constant D in the diffusion equation u_t = D∇²u; sets how quickly spatial gradients are smoothed.
dimensionless number: A ratio of physical quantities that has no units. Characterises the relative importance of different physical effects (e.g. Re, Ma, Q).
dipole: Two closely-spaced monopoles of opposite phase. Radiates in a figure-eight pattern; common model for vibrating surfaces and turbulence-generated sound.
directivity: Angular dependence of a source's radiated field; D(θ) = 1 on-axis, with nulls and sidelobes off-axis.
dispersion: The dependence of wave speed on frequency. In a dispersive medium, different frequency components travel at different speeds, distorting the waveform.
dispersion relation: The relation between frequency ω and wavenumber k for a wave. Non-dispersive: ω = ck. Dispersive: ω(k) is nonlinear.
divergence: A scalar measuring how much a vector field spreads from a point: ∇·v = ∂vₓ/∂x + ∂vᵧ/∂y + ∂v_z/∂z. Positive = source; negative = sink.
domain of dependence: The set of initial-data points that can influence the solution at a given (x,t). For the wave equation: the backward characteristic cone.
Doppler effect: The shift in observed frequency when source and receiver are in relative motion. Approaching → higher pitch; receding → lower pitch. Δf/f ≈ v/c for v ≪ c.
dynamic range: The span between the softest and loudest signals a system can handle. The auditory system covers ~120 dB from threshold to pain.

E

ear canal: The tube about 25 mm long running from the pinna to the eardrum. Its closed-tube resonance amplifies frequencies near 3 kHz.
eardrum: The tympanic membrane: a thin sheet at the inner end of the ear canal that vibrates in response to pressure waves and drives the ossicular chain.
eigenfunction: A function that a linear operator merely multiplies by a scalar: L[f] = λf. Modes of vibration are eigenfunctions of the wave operator.
eigenmode: A natural vibration pattern of a bounded system, corresponding to a specific eigenfrequency. Each eigenmode shape satisfies the boundary conditions.
end correction: The effective lengthening of a tube or pipe beyond its physical end, due to the radiation impedance of the open aperture. Typically ≈0.6× the tube radius.
enthalpy: H = U + PV. The heat content at constant pressure: ΔH = Q_p for isobaric processes. The natural potential for constant-pressure chemistry and engineering.
entropy: A measure of the number of microstates consistent with a macrostate: S = k_B ln Ω. Thermodynamically: dS = δQ_rev/T. Always increases in isolated systems.
equation of state: A relation among state variables (P, V, T, n) that closes the thermodynamic description. Ideal gas: PV = nRT. Real gases: van der Waals, Redlich-Kwong, etc.
equilibrium: A state where all rates of change are zero; the system remains there unless disturbed.
equipartition: Each quadratic degree of freedom in thermal equilibrium carries average energy ½k_BT. Gives heat capacities for ideal gases and harmonic solids.
Euler equation: Newton's second law for an inviscid fluid: ρ Dv/Dt = −∇p. The momentum equation of ideal fluid mechanics.
evanescent wave: Exponentially decaying field beyond a totally-reflecting boundary; carries no net energy.
exponential decay: The solution x(t) = x₀e^{−αt} of dx/dt = −αx. The generic loss process: decay rate proportional to what remains.

F

far field: The region far enough from a source (r ≫ λ and r ≫ source size) that the wavefronts are effectively planar and pressure falls as 1/r.
flux: The flow of a vector field through a surface: ∫∫F·dA. Measures how much of the field passes through the area.
forcing: An external drive applied to a system. The particular solution responds to forcing; the homogeneous solution decays away.
formant: A resonant peak in the spectrum of a vowel. The configuration of mouth and tongue produces F1, F2, F3… which together identify the vowel.
Fourier coefficient: The complex amplitude cₙ of the n-th harmonic in a Fourier series. Extracted by projection: cₙ = (1/T)∫f(t)e^{−inω₀t}dt.
Fourier series: Decomposition of a periodic signal into a sum of sinusoids at multiples of its fundamental frequency.
Fourier transform: A mathematical operation that decomposes a signal into its sinusoidal components. Time-domain ↔ frequency-domain pair.
Fraunhofer diffraction: Far-field diffraction pattern; the angular amplitude is the Fourier transform of the aperture shape.
frequency: The number of oscillation cycles per second, measured in hertz (Hz). For sound, this is what the brain perceives as pitch.
frequency selectivity: The ability to resolve individual frequency components in a complex sound. Determined by cochlear mechanics and the sharpness of basilar-membrane tuning.
Fresnel number: Dimensionless N = a²/(λd) distinguishing near-field (N≫1) from far-field (N≪1) diffraction.
fundamental frequency: The lowest frequency in a periodic signal's Fourier series: f₁ = 1/T where T is the period. All other harmonics are integer multiples.
FWHM: Full Width at Half Maximum — the frequency (or other) interval where a peak exceeds half its peak value.

G

general solution: The full family of solutions to a differential equation, containing as many free constants as the order.
Green's function: The response of a linear system to a unit impulse. Fully characterises propagation from source to receiver in any linear medium.
group velocity: The speed at which a wave packet's envelope (and its energy) travels: v_g = dω/dk. The physically meaningful propagation speed for a signal.

H

Hann window: A raised-cosine window w(n) = ½[1 − cos(2πn/N)] used to reduce spectral leakage in DFT analysis.
harmonic: An integer multiple of the fundamental frequency. The nth harmonic has frequency nf₁. Harmonics are the building blocks of periodic signals.
heat capacity: The energy required to raise a system's temperature by 1 K. C_V (constant volume) and C_P (constant pressure) differ by nR for an ideal gas.
Helmholtz equation: The time-independent wave equation: ∇²u + k²u = 0. Arises from separating the time dependence out of the wave equation for steady-state oscillations.
Helmholtz resonator: A cavity with a narrow neck that resonates at f = (c/2π)√(A/lV), where A is the neck area, l the neck length, V the cavity volume. The acoustic analogue of a mass-spring system.
HRTF: Head-Related Transfer Function. The frequency-dependent filter the head, pinnae, and torso apply between a sound source in space and the eardrum.
Huygens principle: Every point on a wavefront acts as a secondary source of spherical wavelets; the new wavefront is the envelope of all these wavelets.
hyperbolic PDE: A PDE with finite propagation speed (like the wave equation). Information travels along characteristics.

I

ideal gas: A model gas of non-interacting point particles obeying PV = nRT. Valid at low density and high temperature where intermolecular forces are negligible.
impedance: The ratio of a driving quantity to a flow quantity. In acoustics: pressure/velocity. A measure of how strongly a medium resists being moved by a wave.
impedance mismatch: A difference in acoustic impedance between two media at a boundary. The greater the mismatch, the more energy is reflected and the less is transmitted.
impulse response: A system's output when given a single, brief impulse as input. Fully characterises any linear time-invariant system.
inertial cavitation: Explosive growth and violent collapse of a bubble driven by the inertia of the surrounding liquid. Produces extreme local temperatures (~5000 K) and pressures (~GPa).
initial condition: The value(s) of the solution and its derivatives at the starting time: y(0) = y₀, y′(0) = v₀. Picks out a unique solution from the general family.
inverse-square law: Radiated power from a point source falls as 1/r². A consequence of energy spreading over an expanding spherical surface.
irrotational: A vector field with zero curl everywhere (∇×v = 0). Such a field can be written as the gradient of a scalar potential: v = ∇φ.
isothermal: Process at constant temperature; Newton's (incorrect) assumption for sound gave c ≈ 280 m/s in air.

L

Laplace equation: The elliptic PDE ∇²φ = 0. Governs equilibrium fields: steady-state temperature, electrostatic potential, incompressible potential flow.
Legendre polynomial: Orthogonal polynomial P_ℓ(cos θ) solving the angular part of Laplace's equation in spherical coordinates.
Lighthill analogy: Lighthill's reformulation of the Navier-Stokes equations as a wave equation with a quadrupole source term (the Lighthill stress tensor). Foundation of aeroacoustics.
Lighthill stress tensor: Source term T_ij in Lighthill's aeroacoustic analogy; encodes how turbulent flow generates sound.
linear mass density: Mass per unit length μ of a string; enters the 1-D wave speed as c = √(T/μ).
linear time-invariant: A system whose output obeys superposition (linear) and whose behaviour does not change over time (time-invariant). Sinusoids are its eigenfunctions.
linearisation: Replacing a function by its first-order Taylor approximation near a point: f(x) ≈ f(x₀) + f′(x₀)(x−x₀). Valid when |x−x₀| is small.
longitudinal wave: Wave in which particle displacement is parallel to the propagation direction; sound in air is longitudinal.
Lorentzian: The function 1/[(ω−ω₀)² + Γ²]; the spectral shape of a damped resonance, universal near any isolated pole.
LTI system: Linear Time-Invariant system. Fully characterised by its impulse response; output = input * h(t) (convolution).

M

Mach cone: Conical envelope of wavefronts behind a supersonic source; half-angle α = arcsin(1/M).
Mach number: The ratio of flow speed to the local speed of sound: M = v/c. M < 1 is subsonic; M > 1 is supersonic.
material derivative: The time derivative following a fluid element: D/Dt = ∂/∂t + v·∇. Accounts for both local change and advection by the flow.
mean free path: The average distance a molecule travels between collisions: λ = 1/(√2·n·σ). In air at STP: λ ≈ 68 nm.
modal density: The number of resonant modes per unit frequency in an enclosed space. Grows as f² for 3-D rooms; high modal density signals the onset of diffuse-field behaviour.
mode shape: The spatial pattern X_n(x) of a single standing-wave mode; a sinusoidal eigenfunction of the spatial operator.
modulus: The magnitude of a complex number: |z| = √(a² + b²) for z = a + bi. Represents the amplitude when z is a phasor.
monopole: A point source that radiates sound equally in all directions (omnidirectional). The simplest acoustic source; its field falls as 1/r.

N

natural frequency: The frequency at which an undamped system oscillates freely: ω₀ = √(k/m) for a mass-spring. The intrinsic resonance of the system.
Navier-Stokes: The fundamental equations of viscous fluid motion: ρ(Dv/Dt) = −∇P + μ∇²v + f. Newton's second law for a continuum with viscosity μ.
near field: The region close to a source where evanescent components, reactive energy, and complex directivity dominate. Pressure does not fall as a simple power law of r.
nodal line: A curve on a vibrating surface where the displacement is always zero; separates regions oscillating in antiphase.
normal mode: A pattern of motion in which all parts of a system oscillate at the same frequency and in a fixed phase relationship. The building blocks of any vibration.
nucleation: The formation of a new phase (vapour bubble, crystal) from a metastable parent phase. Requires overcoming a free-energy barrier set by surface tension.
Nyquist frequency: Half the sample rate: fₛ/2. The maximum frequency representable without aliasing in a sampled signal.
Nyquist plot: A parametric plot of a complex transfer function in the complex plane as frequency sweeps; used for stability analysis.
Nyquist rate: The minimum sampling rate (2× the highest frequency present) required to perfectly reconstruct a band-limited signal from its samples.

O

octave: Interval corresponding to a 2:1 frequency ratio; the fundamental unit of musical pitch perception.
ossicles: The three smallest bones in the body — malleus, incus, stapes — transmitting motion from the eardrum to the oval window of the cochlea.
overdamped: A damped oscillator with γ > ω₀: returns to equilibrium without oscillating but slower than critical damping. Two real decay rates.
overtone: Any mode of vibration above the fundamental; for strings and tubes the overtones are integer harmonics.

P

P-wave: Primary (longitudinal) elastic wave; particles oscillate along propagation direction. Speed c_P = √((K+4G/3)/ρ).
partial derivative: The derivative of a multivariable function with respect to one variable, holding the others fixed: ∂f/∂x.
particle velocity: The oscillatory velocity of a fluid element as a sound wave passes through it. Related to pressure by Z = p/v in a plane wave.
perturbation: A small deviation from equilibrium; in acoustics, the primed quantities p′, ρ′, v′ riding atop the mean state.
phase transition: A transformation between distinct states of matter (solid, liquid, gas) or order parameters. First-order transitions have latent heat; second-order transitions are continuous.
phase velocity: The speed at which a single-frequency wave's phase fronts travel: v_p = ω/k. May exceed c in dispersive media without violating causality.
phasor: A complex number Ae^{iφ} representing a sinusoidal signal's amplitude A and phase φ. Converts differential equations into algebraic ones by replacing d/dt with iω.
phoneme: The smallest unit of sound that distinguishes meaning in a language (e.g. /b/ vs /p/). English has ~44 phonemes.
plane wave: A wave whose phase fronts are infinite parallel planes; idealisation of a wave from a distant source, valid locally near the listener.
porous absorber: A sound-absorbing material (fibreglass, foam, mineral wool) that converts acoustic energy to heat via viscous drag in its pore network. Effective at high frequencies.
power spectral density: The squared magnitude of a signal's Fourier transform per unit time; gives power per unit frequency.
power spectrum: The distribution of signal power across frequency: |F(ω)|². Its integral equals the total signal energy (Parseval's theorem).
precedence effect: The perceptual rule that the listener attributes the source to the first-arriving wavefront, even when reflections arrive from other directions.
pure tone: A sinusoidal sound at a single frequency. Used in audiometry to measure frequency-specific hearing thresholds.

Q

quadrupole: A source pattern formed by two opposing dipoles. Dominant radiation mechanism of free turbulence (Lighthill stress tensor). Radiated power scales as v⁸/c⁵.
quality factor: Q: a dimensionless measure of resonance sharpness. Equal to center frequency divided by bandwidth. Higher Q = sharper tuning.

R

radiation impedance: Complex impedance seen by a vibrating surface due to the surrounding medium; real part governs radiated power.
radiation pressure: A steady force per unit area exerted by a sound wave on an absorbing or reflecting surface. Proportional to the time-averaged energy density.
random walk: A stochastic process consisting of successive random steps. In the simplest form: ±1 steps with equal probability. The mean displacement grows as √N.
Rankine-Hugoniot: Jump conditions for mass, momentum, and energy across a shock discontinuity in a compressible flow.
rate of change: How quickly a quantity varies with respect to another variable. The derivative gives the instantaneous rate of change.
reactance: The imaginary part X of a complex impedance Z = R + iX; stores energy without dissipating it.
reflection: When a wave hits a boundary between two media, part of its energy turns back into the first medium. R = (Z2 − Z1)/(Z1 + Z2).
reflection coefficient: The ratio of reflected to incident wave amplitude at a boundary: R = (Z2 − Z1)/(Z1 + Z2). Ranges from −1 (soft boundary) to +1 (rigid boundary).
refraction: The bending of a wave as it passes between regions of different propagation speed. Governed by Snell's law: sin θ₁/c₁ = sin θ₂/c₂.
relaxation time: Characteristic time τ for energy transfer between molecular degrees of freedom; sets absorption peak frequency.
resonance: The condition where a driving frequency matches a system's natural frequency, producing maximum response amplitude.
restoring force: Force directed toward equilibrium, proportional to displacement for small perturbations (F = −kx).
reverberation: The collection of reflections that follows a direct sound in a room, gradually decaying. Characterised by reverberation time T60.
reverberation time: T60: the time for sound energy to decay by 60 dB after the source stops. Related to room volume and absorption: T60 = 0.161V/A (Sabine equation).
Reynolds number: Re = ρvL/μ. The ratio of inertial to viscous forces. Re ≪ 1: Stokes flow (viscosity dominates). Re ≫ 1: inertia dominates, turbulence possible.
room mode: A resonant standing-wave pattern in an enclosed space, determined by the room geometry. At low frequencies, individual modes are audible as peaks/dips.
root-mean-square: The square root of the time-averaged square of a signal: f_rms = √((1/T)∫f²dt). For a sinusoid, amplitude/√2.

S

Sabine equation: T60 = 0.161V/A, where V is room volume (m³) and A is total absorption (m² sabins). The first quantitative model of room reverberation (W.C. Sabine, 1898).
sample rate: Samples per second f_s when digitising a signal; must exceed 2× the maximum frequency to avoid aliasing.
Schroeder frequency: The crossover frequency above which a room's modal spacing is dense enough that the sound field is statistically diffuse: f_S ≈ 2000√(T60/V).
separation constant: The shared constant that both sides of a separated PDE must equal; becomes the eigenvalue of the spatial problem.
separation of variables: A PDE-solving technique that assumes the solution factors as u(x,t) = X(x)·T(t), reducing one PDE to two ODEs. Works when the operator and domain allow it.
shock wave: A thin region of abrupt pressure, density and temperature change propagating supersonically. Nonlinear steepening of a large-amplitude wave into a discontinuity.
short-time Fourier transform: Windowed Fourier transform giving local spectral content; the basis of spectrogram computation.
simple harmonic motion: Oscillation governed by ẍ = −ω₀²x. Solution: x(t) = A cos(ω₀t + φ). The linearised dynamics near any stable equilibrium.
sinc function: sinc(x) = sin(πx)/(πx). The Fourier transform of a rectangular pulse and the ideal interpolation kernel for band-limited reconstruction.
sinusoid: A function of the form A sin(ωt + φ) or equivalently A cos(ωt + φ). The basic periodic waveform; all Fourier components are sinusoids.
Snell's law: The law of refraction: sin θ₁/c₁ = sin θ₂/c₂, relating the angles of incidence and transmission to the wave speeds in the two media.
sonic boom: The impulsive sound heard when a shock wave from a supersonic object reaches the observer. A Mach cone sweeps along the ground as the object passes.
sonoluminescence: Light emission from a collapsing cavitation bubble, caused by extreme heating of the gas during the final stage of inertial collapse.
specific heat ratio: γ = cₚ/cᵥ; ratio of heat capacities. For diatomic air γ = 1.4; enters sound speed as c = √(γRT/M).
spectrogram: Time-frequency image formed by computing short-time Fourier transforms of successive windowed signal segments.
spectrum: The frequency-domain representation of a signal: the set of amplitudes and phases at each frequency component.
speed of sound: The propagation speed of small-amplitude pressure disturbances. ≈343 m/s in air at room temperature, ≈1480 m/s in water.
spherical harmonic: Eigenfunction Y_ℓm(θ,φ) of the angular Laplacian on the sphere; the angular modes in spherical geometry.
spherical wave: A wave radiating outward from a point source, with amplitude falling as 1/r.
standing wave: A wave pattern formed by superposition of two waves traveling in opposite directions. Characterised by fixed nodes (zero amplitude) and antinodes (maximum amplitude).
steady state: The long-time behaviour of a driven system after transients have died away. For a sinusoidally driven linear system, it oscillates at the driving frequency.
STRF: Spectro-Temporal Receptive Field. The 2-D function (frequency × time) characterising what stimulus features drive a cortical neuron.
Strouhal number: Dimensionless St = fd/U relating vortex-shedding frequency to flow speed and body size; St ≈ 0.2.
superposition: The principle that solutions of a linear equation can be added to give new solutions. The foundation of Fourier methods and modal analysis.
surface tension: The energy per unit area (or force per unit length) at a liquid interface, arising from the cohesive deficit of surface molecules. Units: N/m or J/m².

T

tension: Force per unit cross-section along a string or membrane; sets the wave speed via c = √(T/μ).
timbre: Perceptual quality distinguishing sounds of the same pitch and loudness; determined by spectral envelope shape.
time constant: τ = 1/α: the time for an exponentially decaying quantity to fall to 1/e ≈ 37% of its initial value.
time-harmonic: Oscillating at a single frequency; a field of the form φ(r)e^{−iωt}, reducing the wave equation to Helmholtz.
total internal reflection: Complete reflection when a wave hits a boundary beyond the critical angle; no transmitted wave exists.
transfer function: The frequency-domain ratio of output to input phasor: H(ω) = Y(ω)/X(ω). Fully characterises a linear system's frequency response.
transmission coefficient: The fraction of incident wave energy that passes through a boundary or barrier into the second medium. T = 1 − R² for lossless interfaces.
turbulence: Chaotic, three-dimensional fluid motion characterised by eddies at many scales, enhanced mixing, and energy cascade from large to small scales.

U

uncertainty principle: A signal cannot be simultaneously narrow in time and narrow in frequency. Time-bandwidth product has a minimum, saturated by the Gaussian.
underdamped: A damped oscillator with γ < ω₀: oscillates with exponentially decaying amplitude. The most common regime for musical and biological systems.

V

velocity potential: A scalar field φ such that v = ∇φ. Exists when the flow is irrotational. Central to linearised acoustics.
volume velocity: The product of particle velocity and cross-sectional area (U = v·A). The acoustic analogue of electric current in lumped-element circuit models.
von Kármán vortex street: Alternating pattern of vortices shed behind a bluff body in a flow; source of aeolian tones.

W

wave equation: A second-order PDE describing how a disturbance propagates. For pressure in air: ∂²p/∂t² = c²∇²p.
wavefront: A surface of constant phase in a propagating wave. Plane waves have flat wavefronts; point sources have spherical wavefronts.
wavenumber: The spatial frequency of a wave: k = 2π/λ. Higher k means shorter wavelength and more rapid spatial oscillation.
wavevector: Vector k pointing in propagation direction with magnitude 2π/λ; encodes spatial periodicity and direction.
window function: A tapering function (Hann, Hamming, Blackman, etc.) multiplied with a signal segment before DFT to reduce spectral leakage at the cost of frequency resolution.