Waves, Oscillations & Acoustics

Absorption Coefficient

The fraction of incident sound energy absorbed by a material surface rather than reflected.

α = I_absorbed / I_incident (0 ≤ α ≤ 1) Dimensionless

Acoustic Impedance

The physical opposition offered by a medium to sound wave flow, defined as ratio of acoustic pressure to particle velocity.

Z = ρ v_sound Pa·s/m (Rayls)

Waves, Oscillations & Acoustics

Acoustic Power

The total sound energy emitted by an acoustic source per unit time in all directions.

P_ac = ∫ I · dA = 4π r² I W

Waves, Oscillations & Acoustics

Acoustic Resonance

The amplification of sound waves within a hollow cavity or tube when driven at frequencies matching cavity standing wave modes.

f_n = n v / (2 L) Hz

Waves, Oscillations & Acoustics

Angular Frequency

A scalar measure of rotation or oscillation rate expressed in radians per unit time.

ω = 2π f = 2π / T rad/s

Waves, Oscillations & Acoustics

Beats

The periodic volume fluctuation or throbbing sound produced by the interference of two sound waves with slightly different frequencies.

f_beat = |f1 - f2| Hz

Waves, Oscillations & Acoustics

Closed Organ Pipes

An acoustic pipe closed at one end and open at the other, having a displacement node at the closed end and an antinode at the open end.

f_n = n v / (4 L) (n = 1, 3, 5, ...) Hz

Waves, Oscillations & Acoustics

Compound Pendulum

A rigid body suspended from a fixed horizontal axis that oscillates under gravity about a pivot point.

T = 2π √(I / (m g d)) s

Waves, Oscillations & Acoustics

Constructive & Destructive Interference

The phenomenon where overlapping coherent waves combine to reinforce (constructive) or cancel (destructive) each other's amplitude.

Path Diff ΔL = m λ (Constructive), ΔL = (m + ½) λ (Destructive) m

Waves, Oscillations & Acoustics

Damped Oscillations

Oscillatory motion whose mechanical energy and amplitude decrease exponentially over time due to dissipative forces like friction or…

x(t) = A exp(-b t / 2m) cos(ω_d t + φ) m

Waves, Oscillations & Acoustics

Decibel Scale

A logarithmic scale used to express sound intensity or sound pressure level relative to a reference threshold.

β = 10 log10(I / I0), I0 = 10⁻¹² W/m² dB

Waves, Oscillations & Acoustics

Doppler Effect

The apparent shift in observed wave frequency caused by relative motion between the wave source and the observer.

f_obs = f_src (v ± v_obs) / (v ∓ v_src) Hz

Waves, Oscillations & Acoustics

Echo

A distinct reflected sound wave received at the listener's ear with sufficient time delay after the direct sound.

d = v t / 2 m

Waves, Oscillations & Acoustics

End Correction

An acoustic correction applied to resonance pipe lengths to account for displacement antinodes forming slightly outside the open pipe ends.

e ≈ 0.6 r, L_effective = L + 0.6 r (One Open End) m

Waves, Oscillations & Acoustics

Forced Oscillations

Oscillations produced in a system subjected to a periodic external driving force.

m (d²x/dt²) + b (dx/dt) + k x = F0 cos(ω t) m

Waves, Oscillations & Acoustics

Frequency

The number of complete wave cycles or vibrational repetitions occurring per unit time.

f = 1 / T = v / λ Hz (s⁻¹)

Waves, Oscillations & Acoustics

Fundamental Frequency

The lowest natural frequency at which a standing wave pattern can be established in a vibrating system.

f1 = v / (2 L) (String / Open Pipe) Hz

Waves, Oscillations & Acoustics

Group Velocity

The velocity at which the overall envelope shape of a wave packet travels through space, representing energy transport speed.

v_g = dω / dk m/s

Waves, Oscillations & Acoustics

Harmonics

Resonant frequencies of a system that are integer multiples of its fundamental frequency.

f_n = n f1 (where n = 1, 2, 3, ...) Hz

Waves, Oscillations & Acoustics

Huygens-Fresnel Principle

The wave propagation principle asserting that every point on a wavefront acts as a secondary source of spherical wavelets.

New Wavefront = Envelope of Secondary Wavelets N/A

Waves, Oscillations & Acoustics

Lissajous Figures

Complex geometric curves traced by combining two perpendicular simple harmonic oscillations.

x(t) = A sin(a t + δ), y(t) = B sin(b t) N/A

Waves, Oscillations & Acoustics

Longitudinal Wave

A wave in which medium particles oscillate parallel to the direction of wave energy propagation.

s(x,t) = s_max cos(k x - ω t) m

Waves, Oscillations & Acoustics

Loudness

The subjective human psychological sensation of sound strength, depending on physical intensity and ear frequency response.

Loudness ∝ log10(I / I0) Sone (or Phon)

Waves, Oscillations & Acoustics

Mach Number

A dimensionless speed ratio equal to the speed of an object or fluid divided by local speed of sound in the surrounding medium.

M = v / v_sound Dimensionless