Speed of Sound in Air, Solids, and Electrical Signals | Acoustics Tutorial

Multi-microphone recording creates phase issues when sound arrives at different times due to varying distances. This causes destructive interference, thinning the recorded sound. Delay compensation virtually aligns microphones by shifting samples, compensating for sound speed (340 m/s). This technique allows engineers to achieve accurate sound reproduction even when perfect microphone placement is impossible, significantly improving recording quality.

Beyond MS, additional microphones (overhead, body, room) can capture different aspects of a sound source, creating a larger apparent size while maintaining phase coherence. Pro Tools provides visual feedback (cubes with numbers) showing phase relationships and latency compensation status. The software uses a traffic light system: green (relaxed), yellow (approaching limits), red (cannot compensate). Pro Tools HD has a more powerful compensation engine than standard Pro Tools.

When using multiple microphones (boom and lavs), there will be latency and phase discrepancies between tracks. Boom mics are further back and will have more delay than lav mics, which are on actors' bodies. This creates an echo-like effect that must be addressed through phase alignment.

Microphone placement significantly impacts sound quality, with small adjustments recovering 6 dB of energy. Phase alignment between multiple microphones on the same source is critical for a unified sound. Engineers must compensate for latency introduced by signal routing and external triggers (5-6 milliseconds), typically by delaying all channels except the trigger. The goal is ensuring all elements arrive simultaneously for a cohesive sound image.

Phase alignment is the process of correcting time and polarity differences between multiple microphone signals to prevent recordings from sounding thin or weak; automatic phase alignment tools like Aligner analyze and adjust the timing (in samples) of each track so that signals from different microphones arrive at the same point in time, resulting in a fuller, more cohesive sound.

Standing wave frequencies can be calculated using the speed of sound. In metric units, divide 340 m/s by wall distance in meters; in imperial units, divide 1,000 ft/s by distance in feet. For example, 5-meter walls yield 68 Hz, 6.8-meter walls yield 50 Hz. Problem frequencies include these values and their harmonics (25, 50, 100 Hz). A standard box-shaped room has three primary modes from long walls, short walls, and ceiling-floor distances. When these frequencies have mathematical relationships, audible problems occur. Complete elimination requires removing walls or adding absorbing materials, which is impractical for most rooms. Professional solutions involve specialized construction up to 50 cm deep. Architects should avoid problematic room ratios during design.

Room mode frequencies are calculated using the formula: f = (c/2)√[(p/L)² + (q/W)² + (r/H)²], where c is the speed of sound, L, W, and H are room dimensions, and p, q, r are mode numbers (0, 1, 2, 3...). This formula calculates the frequency at which standing waves form for each mode. The mode numbers indicate how many half-wavelengths fit between each pair of parallel surfaces.

Room modes occur when sound frequencies resonate between parallel surfaces. The formula is: frequency = speed of sound (343 m/s) / (2 × distance). For a 3m room, modes occur at 28.5 Hz, 56 Hz, and 112 Hz. Square rooms are problematic because modes from different dimensions align, creating cumulative issues. Non-square rooms with different dimensions prevent mode alignment. Testing involves generating sine waves at calculated frequencies and walking through the room to identify nodes (quiet areas) and anti-nodes (loud areas).

Axial room modes are calculated using the formula f = v/(2L), where v is the speed of sound (approximately 1125.2 ft/s) and L is the distance between parallel surfaces. The fundamental mode represents half-wavelength fitting in the room, with harmonic modes being integer multiples (2x, 3x, 4x...). For a 20-foot wall, the fundamental mode is 28.13 Hz, with harmonics at 56.26 Hz, 84.39 Hz, and so on. Only frequencies below the Schroeder frequency require special attention as higher frequencies behave as ray energy.

This comprehensive process involves four key steps: (1) Measure room dimensions from wall to wall, obtaining length, width, and ceiling-to-floor height; (2) Convert all measurements to meters by dividing feet by 3.28; (3) Calculate the fundamental frequency for each dimension using the formula: fundamental frequency = speed of sound (344 m/s) ÷ wavelength (in meters); (4) Derive higher-order modes by multiplying the fundamental frequency by 0.5, 1, 1.5, and 2 for the first through fourth modes respectively. This manual calculation method allows acoustic engineers and enthusiasts to predict and analyze room resonance characteristics without specialized software.

This section covers the foundational concepts of acoustical transduction—the conversion between sound (acoustic) energy and electrical energy. The lecture explains why transduction is necessary for processing sound signals electronically, as all modifications must occur in electrical circuits. Two physical principles govern transducer operation: electrodynamics (using magnetic fields where F = B × l × i and V = B × l × u) and electrostatics (using variable capacitance where F = (ε × A × V²) / (2x²)). The transducer is modeled as a two-port network with electrical and mechanical ports, characterized by four key impedances: Zeb (blocked electrical), Zef (free electrical), Zms (short-circuit mechanical), and Zmo (open-circuit mechanical). These concepts form the theoretical foundation for understanding microphone and loudspeaker design.

Transducer education encompasses three physics domains: electromechanical (energy-to-signal conversion), electrostatics (charged plates and membranes), and electromagnetics (coils and magnets). Practical implementation requires understanding how loudspeakers and microphones convert between acoustic and electrical domains. Students must consider entire systems—including plates as edge-supported membranes, vibrational modes, and acoustic cavity interactions—rather than isolated components. Experimental methodology involves systematic variable selection (string tension, can size), third-octave band measurements, and comparison of theoretical predictions with empirical results. Historical research into devices like Thomson's water microphone and hot wire microphones grounds practical work in foundational principles. Comprehensive testing includes impedance measurements, sensitivity testing, frequency response characterization, and total harmonic distortion analysis.

A transducer is a device that translates electrical signals into acoustic waves or vice versa. Speakers are transducers that convert voltage into sound pressure waves in the air. Microphones function as transducers in reverse, converting acoustic pressure waves into electrical signals. The eardrum also acts as a transducer, converting sound in the air into vibrations that travel through the middle ear bones into the fluid-filled inner ear.

Electroacoustics involves the conversion between acoustic and electrical domains using transducers, which operate on electromagnetic or electrostatic principles; microphones are characterized by their frequency response (flat for measurement, colored for music) and directivity, while loudspeakers require multiple drivers to cover the full audible range (20 Hz to 20 kHz) due to diaphragm vibration limitations at high frequencies.

Speakers and microphones are common examples of transducers. When electrical energy is supplied to speakers, they convert it into acoustic energy (sound). Conversely, when acoustic energy (sound) is supplied to microphones, they convert it into electrical energy. This bidirectional conversion allows us to record sound or amplify it through speakers.