Acoustics and Sound Physics

Introduction to Acoustics

Acoustics is the branch of physics concerned with the study of mechanical waves in gases, liquids, and solids—including their generation, propagation, reflection, absorption, and detection. Sound waves are longitudinal pressure perturbations propagating through a compressible medium at the speed of sound c = sqrt(B/rho) (B = bulk modulus, rho = density)—approximately 343 m/s in air at 20°C, 1480 m/s in water, and 5120 m/s in steel. The human auditory system responds to frequencies from ~20 Hz (infrasound threshold) to ~20 kHz (upper ultrasound threshold), with pressure amplitude sensitivity spanning six orders of magnitude—from the threshold of hearing (20 micropascal) to the threshold of pain (~20 Pa).

Acoustics interfaces with almost every domain: architectural acoustics designs concert halls and noise-controlled spaces; medical ultrasound uses MHz-frequency sound waves for imaging tissues and destroying tumours; underwater acoustics enables sonar, ocean monitoring, and cetacean communication research; musical acoustics connects physics to art through the vibration modes of instruments; noise control engineering protects workers and communities from harmful sound exposure; and infrasound monitoring detects nuclear explosions and volcanic eruptions at continental distances. The physics of waves—superposition, interference, diffraction, resonance, and nonlinear propagation—all manifest in acoustic systems with experimentally accessible laboratory demonstrations.

Wave Properties of Sound

Reflection, Refraction, and Diffraction

Sound obeys the same wave reflection laws as light at interfaces: angle of incidence equals angle of reflection. Acoustic mirrors, acoustic lenses, and concave reflectors focus sound energy. Total internal reflection of sound occurs when the grazing angle exceeds the critical angle for media with different sound speeds—creating acoustic waveguides in the ocean (SOFAR channel at ~1000m depth) where sound speed has a minimum enabling long-distance propagation with minimal spreading losses (sound has been detected at 20,000 km range using SOFAR). Diffraction—wave bending around obstacles and through apertures—determines acoustic behaviour in room acoustics and sound directivity. Acoustic diffusers in concert halls exploit diffraction from surface irregularities to uniformly scatter sound energy improving spatial impression and reducing echo coherence.

Resonance and Standing Waves

Resonance occurs when driving frequency matches a system's natural frequency, building large oscillation amplitude. Acoustic resonance in cavities and enclosures creates standing waves at discrete frequencies f_n = n*c/(2L) (pipe open at both ends) or f_n = (2n-1)*c/(4L) (pipe closed at one end). Room modes (axial, tangential, oblique) create uneven frequency response in small rooms—audible as booming bass at certain positions. The Helmholtz resonator (cavity with neck) resonates at f = (c/2pi) * sqrt(A/(V*L)) (A=neck area, V=volume, L=neck length)—the mechanism explaining guitar body and instrument port resonances, and exploited in bass reflex loudspeaker enclosures and automotive exhaust mufflers. Acoustic metamaterials with engineered resonator arrays achieve negative effective mass density or negative bulk modulus enabling sound cloaking, sub-wavelength superfocussing, and perfect sound absorbers.

Ultrasound Physics and Applications

Medical Ultrasound

Diagnostic medical ultrasound uses piezoelectric transducers generating 2–15 MHz pressure pulses sent into tissue—echoes from acoustic impedance boundaries (Z = rho*c) between different tissues are received and time-gated to build images (pulse-echo B-mode). Image resolution is approximately half the acoustic wavelength (~0.1–0.5 mm at medical frequencies); penetration depth decreases with frequency due to attenuation (approximately 0.5 dB/cm/MHz in soft tissue). Doppler ultrasound measures blood flow velocity from frequency shifts of echoes from moving red blood cells (f_Doppler = 2*f*(v/c)*cos(theta)). High-intensity focused ultrasound (HIFU) converges beams to a focal spot of ~1 mm3 reaching temperatures of 60-80°C causing coagulative necrosis—used for non-invasive ablation of prostate cancer, fibroids, and brain tumours (ExAblate Neuro through the intact skull). Contrast-enhanced ultrasound uses gas-filled microbubbles resonating at ultrasound frequencies to improve vessel visualisation and enable targeted drug delivery.

Architectural and Room Acoustics

Room acoustics determines the auditory character of concert halls, recording studios, theatres, and classrooms. Key parameters: reverberation time T60 (Sabine's formula T60 = 0.161*V/A, volume/absorption); clarity C80 (ratio of early energy within 80ms to late energy); strength G (level relative to free field); and lateral energy fraction LEF (spaciousness impression). Optimal T60 for symphonic music (~2 seconds for halls ~2000 seats) differs from opera (1.5s) and speech (0.6-0.8s). Wave-based acoustic modelling (finite element method, boundary element method) accurately predicts room acoustics below ~500 Hz where geometric ray-tracing approximations fail. Active noise cancellation in aircraft cabins, open-plan offices, and headphones uses digital signal processing and secondary loudspeakers to generate anti-phase pressure waves cancelling primary noise at the listener position—effective for tonal and low-frequency noise.

Examples and Applications

Example 1: Acoustic Levitation

Acoustic radiation pressure—the time-averaged force exerted by high-intensity standing waves—can levitate objects at pressure nodes of ultrasonic standing waves where radiation force balances gravity. Acoustic levitation has levitated water drops, small biological samples, electronics, and drug particles for contactless manipulation and processing. The levitation force scales with acoustic intensity and object volume; maximum levitatable mass is limited by available acoustic intensity. Applications include containerless processing of molten materials avoiding container contamination, bioreactor cell culture without mechanical agitation stress, and cosmic dust analogue formation studies in microgravity simulation. Single beam acoustic tweezers (using focused transducers with vortex phase patterns) can trap and translate objects in 3D—analogous to optical tweezers but effective for larger objects and turbid media inaccessible to optical approaches.

Example 2: Sonoluminescence

Sonoluminescence—the emission of light pulses from acoustically driven collapsing bubbles—is one of the most dramatic energy concentration phenomena in physics. A single bubble trapped in a standing acoustic wave at ~25 kHz collapses adiabatically from ~50 micrometers to ~0.5 micrometers in microseconds, reaching internal temperatures estimated at 10,000–100,000 K and pressures above 1000 atm before rebounding—emitting picosecond-duration light flashes repeatable each acoustic cycle. The energy focusing from bubble collapse concentrates acoustic energy by over 10 orders of magnitude. Some researchers have proposed bubble fusion (Taleyarkhan controversy 2002)—claims of neutron emission from sonoluminescence in deuterated acetone—remain highly contested and unreplicated. Sonoluminescence is used as a probe of extreme high-pressure, high-temperature conditions and in sonochemistry where cavitation bubble collapse drives chemical reactions impossible at ambient conditions.

Example 3: Seismoacoustics and Infrasound

Infrasound—acoustic frequencies below 20 Hz—propagates with very low attenuation over thousands of kilometres through the atmosphere and ocean. The Comprehensive Nuclear-Test-Ban Treaty Organisation (CTBTO) operates a global infrasound monitoring network (IMS—International Monitoring System) with 60 arrays detecting nuclear explosions, volcanic eruptions, large meteorite impacts, and severe weather through infrasound signatures. The 2013 Chelyabinsk meteor generated infrasound detected globally; Krakatoa in 1883 created infrasound that circled Earth 5 times. Microbaroms—continuous infrasound generated by ocean swell interaction—provide persistent background signals against which discrete events are identified. Coupled seismo-acoustic monitoring—measuring pressure waves transferring between ground and atmosphere at terrain features—helps distinguish underground nuclear tests from natural seismic events in treaty verification.

Example 4: Musical Acoustics

Musical instruments are precision acoustic resonators exploiting specific vibrational modes. String instruments: standing waves on strings (f_n = n/(2L) * sqrt(T/mu), T=tension, mu=linear density) generate harmonics; the soundboard radiates acoustic energy. Woodwinds: standing waves in cylindrical (clarinet—odd harmonics only) or conical (oboe, saxophone—all harmonics) bores selectively amplified by register keys. Brass instruments: player lip vibration excites resonant air column modes—valves change tube length shifting resonances. Acoustic guitar radiation: body modes couple string vibration to air radiation through soundhole and top plate vibrations—finite element modelling guides modern instrument designs. Non-Western tuning systems based on just intonation rather than equal temperament have different mathematical relationships between notes—a rich intersection of physics and cultural music theory. Psychoacoustics: equal-loudness contour (Fletcher-Munson curves), pitch perception, and consonance/dissonance perception arise from cochlear mechanics and neural processing.

Example 5: Underwater Acoustics and Sonar

Sound is the primary information-carrying wave in the ocean—light attenuates within metres while sound propagates thousands of kilometres. Sonar (Sound Navigation And Ranging) uses active (transmit-receive) or passive (receive-only) acoustic systems for submarine detection, bathymetry, fish finding, and ocean monitoring. Sound speed in seawater depends on temperature, salinity, and pressure: c = 1449 + 4.6T - 0.055T^2 + 0.00029T^3 + (1.34 - 0.01T)(S-35) + 0.016P (Mackenzie equation). The SOFAR channel (Sound Fixing And Ranging)—minimum sound speed layer at ~1000m—ducts low-frequency sound (20-500 Hz) to intercontinental distances: the acoustic thermometry of ocean climate (ATOC) project propagated sound from Heard Island to California (18,000 km) measuring ocean warming through travel time changes. Marine bioacoustics: blue whales produce the loudest biological sounds (up to 188 dB re 1 micropascal) communicating across ocean basins; anthropogenic noise pollution from shipping, sonar, and seismic surveys disrupts cetacean communication and navigation.

Example 6: Noise Control Engineering

Noise—unwanted sound—causes hearing damage (NIHL—noise-induced hearing loss occurs above 85 dB(A) sustained exposure), cardiovascular disease, cognitive impairment in children, and economic losses. Engineering noise control hierarchy: noise source control (quieter machinery, aerodynamic redesign of fans and exhausts); transmission path control (barriers, enclosures, vibration isolation, acoustic panels); receiver protection (hearing protection, active noise control). The decibel scale (dB = 10*log10(I/I_0)) compresses the 10^12 intensity range of hearing to 0-120 dB for A-weighted (dBA—frequency-weighted to match hearing sensitivity) noise level. EU Noise Directive requires environmental noise mapping and action plans for urban areas above 55 dB Lden. Wind turbine noise—primarily trailing-edge boundary layer aerodynamic noise—is subject to strict setback rules in many jurisdictions (IEC 61400-11 measurement standard).

Example 7: Acoustic Emission and NDT

Acoustic emission (AE) testing detects transient elastic waves generated by crack growth, fibre fracture, dislocation movement, and phase transformations in materials under stress—a passive non-destructive testing method for structural health monitoring. AE sensors (piezoelectric accelerometers, MEMS devices) placed on structures detect the elastic wave bursts emitted when damage accumulates; source localisation from arrival time differences between sensor array elements pinpoints damage location in real time. Pressure vessels, aircraft structures, composite wind turbine blades, and bridges are monitored by AE systems detecting fatigue crack growth long before failure. Acoustic microscopy: focused ultrasound beams at 10–2000 MHz scan material interiors at optical-like resolution, revealing subsurface cracks, delaminations, and density variations invisible on surfaces—critical for quality control of semiconductor packages, turbine blade coatings, and biomedical implant bonding.

Example 8: Thermoacoustics

Thermoacoustics—the conversion between acoustic work and heat—enables heat engines and refrigerators with no moving parts except the resonating gas itself. A thermoacoustic engine has a stack (porous material inside an acoustic resonator) with a temperature gradient; gas parcels oscillating in the sound wave experience a thermodynamic cycle—absorption/rejection of heat at different phases producing net acoustic power. The reverse process is a thermoacoustic refrigerator: acoustic power drives gas parcels to pump heat from cold to hot end without a compressor or working fluid, using noble gas or air. Los Alamos National Laboratory built thermoacoustic engines running on solar heat and a refrigerator cooling to -65°C. Ben and Jerry's ice cream factories tested thermoacoustic freezers. Their simplicity, no-moving-parts reliability, and ability to use any heat source (including waste heat) make them attractive for remote power generation and liquefaction of natural gas aboard LNG ships.

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