Waves, Oscillations & Acoustics — 53 Terms Defined

Nodes & Antinodes Waves, Oscillations & Acoustics m Specific fixed positions on a standing wave where displacement amplitude is zero (nodes) or maximum (antinodes). Node Spacing = λ / 2, Antinode Spacing = λ / 2

Non-linear Oscillations Waves, Oscillations & Acoustics Various Oscillatory systems where restoring forces do not obey linear Hooke's law, leading to amplitude-dependent frequency and chaotic behavior. m (d²x/dt²) + k x + β x³ = 0 (Duffing Equation)

Normal Modes Waves, Oscillations & Acoustics Hz Characteristic independent natural patterns of motion in which all parts of an oscillating system move sinusoidally at the same natural frequency. f_n = n f1 = n v / (2 L)

Open Organ Pipes Waves, Oscillations & Acoustics Hz A cylindrical acoustic pipe open at both ends, containing displacement antinodes at both openings. f_n = n v / (2 L) (n = 1, 2, 3, ...)

Overtones Waves, Oscillations & Acoustics Hz Any resonant frequency higher than the fundamental frequency in a musical sound. First Overtone = 2nd Harmonic (for strings)

Phase Waves, Oscillations & Acoustics rad (radians) The fractional position of a point within a wave cycle, expressed as an angle relative to a reference origin. Φ(x,t) = k x - ω t + φ0

Phase Difference Waves, Oscillations & Acoustics rad (radians) The angular difference between corresponding points on two waves or between different points on a single wave. Δφ = (2π / λ) Δx = (2π / T) Δt

Phase Velocity Waves, Oscillations & Acoustics m/s The speed at which a single monochromatic wave crest or phase front advances through a medium. v_p = ω / k = f λ

Pitch Waves, Oscillations & Acoustics Hz (or Musical Notes) The subjective psychoacoustic perception of a sound's frequency by human listeners. Pitch ∝ f

Principle of Superposition Waves, Oscillations & Acoustics m The principle stating that when two or more linear waves overlap at a point, total resultant displacement equals vector sum of individual displacements. y_total(x,t) = y1(x,t) + y2(x,t) + ... + yn(x,t)

Resonance Waves, Oscillations & Acoustics Hz The phenomenon where an oscillating system driven at its natural frequency absorbs maximum energy, resulting in large-amplitude vibrations. f_driven = f_natural = (1 / 2π) √(k / m)

Reverberation Waves, Oscillations & Acoustics s The persistence of sound in an enclosed space caused by multiple continuous reflections from room boundaries after the original source stops. RT60 = 0.161 V / A (Sabine's Formula)

Shock Wave Waves, Oscillations & Acoustics Pa A extremely thin propagating pressure disturbance characterized by a nearly instantaneous jump in pressure, temperature, and density. P2 / P1 = 1 + (2γ / (γ + 1)) (M1² - 1)

Sonar Waves, Oscillations & Acoustics m Sound Navigation and Ranging—a technique utilizing acoustic wave propagation underwater to navigate, communicate, or detect objects. d = v_water t / 2

Sonic Boom Waves, Oscillations & Acoustics dB / Pa An explosive impulsive acoustic thunderclap heard on the ground when an object travels faster than the speed of sound. sin α = 1 / M (Mach Cone Angle)

Sound Intensity Waves, Oscillations & Acoustics W/m² The time-averaged rate of sound energy flow per unit area perpendicular to the direction of propagation. I = P / A = p_rms² / (ρ v)

Speed of Sound Waves, Oscillations & Acoustics m/s The speed at which a pressure wave travels through an elastic medium. v = √(K / ρ) (Fluids), v = √(γ R T / M) (Ideal Gas)

Standing Waves Waves, Oscillations & Acoustics m A stationary wave pattern formed by the superposition of two identical waves traveling in opposite directions along the same medium. y(x,t) = [2 A sin(k x)] cos(ω t)

Threshold of Hearing Waves, Oscillations & Acoustics W/m² (0 dB) The minimum sound pressure level or intensity audible to a healthy human ear at 1000 Hz. I0 = 10⁻¹² W/m² (0 dB SPL, P0 = 20 µPa)

Threshold of Pain Waves, Oscillations & Acoustics W/m² (120-130 dB) The upper sound intensity limit above which acoustic vibrations cause physical discomfort and immediate structural damage to human ears. I_pain ≈ 1 W/m² (120 - 130 dB SPL)

Timbre Waves, Oscillations & Acoustics N/A The subjective tone quality or color of a musical sound that distinguishes different instruments playing the same fundamental pitch and loudness. Fourier Spectrum Balance

Transverse Wave Waves, Oscillations & Acoustics m A wave in which medium particles oscillate perpendicular to the direction of wave energy propagation. y(x,t) = A sin(k x - ω t)

Tsunami Waves, Oscillations & Acoustics m/s A series of extremely long-wavelength ocean water waves generated by sudden vertical displacement of the seafloor. v = √(g d)

Van der Pol Oscillator Waves, Oscillations & Acoustics N/A A non-linear oscillator with non-linear damping that exhibits stable self-sustained limit cycle vibrations. d²x/dt² - μ (1 - x²) dx/dt + x = 0