Electronics Guide

Measurement Principles

An ideal impulse contains all frequencies at equal amplitude and zero phase, occurring at a single instant in time. In practice, creating such a signal with sufficient energy proves impossible, so measurement techniques use specialized signals that can be processed to extract the impulse response. The captured response shows the direct sound arrival followed by early reflections from nearby surfaces, transitioning into the diffuse reverberant field as reflections multiply and overlap.

The measurement chain typically includes an omnidirectional sound source, a calibrated measurement microphone, and a digital acquisition system. Source directivity affects which room surfaces contribute to the measured response. Receiver position determines the balance between direct and reflected sound. Multiple source-receiver combinations characterize the room's spatial variation.

Logarithmic Swept Sine Technique

The logarithmic swept sine (also called exponential sine sweep or ESS) has become the preferred method for room impulse response measurement. A sine wave sweeps continuously from low to high frequency, typically spanning 20 Hz to 20 kHz over several seconds. The logarithmic frequency progression ensures equal energy per octave, matching the ear's logarithmic frequency perception.

Deconvolution of the recorded sweep with an inverse filter yields the impulse response. The technique provides excellent signal-to-noise ratio because energy accumulates over the sweep duration rather than concentrating in a brief impulse. Additionally, harmonic distortion products separate in time from the fundamental response, appearing as distinct pre-echoes that can be windowed out. This distortion separation makes swept sine measurement particularly valuable for characterizing rooms with powerful sound systems.

Maximum Length Sequence

Maximum length sequence (MLS) measurement uses a pseudorandom binary signal with special correlation properties. Cross-correlating the recorded signal with the original MLS stimulus extracts the impulse response. The technique offers fast measurement and good noise rejection, with measurement time limited only by the desired frequency resolution.

However, MLS has significant limitations. Time-varying conditions (moving air, audience movement, system nonlinearity) spread energy throughout the recovered response rather than concentrating it at the correct arrival times. Harmonic distortion also disperses into the response rather than separating as with swept sine measurement. These issues have led most practitioners to prefer logarithmic sweeps for precision room measurement, though MLS remains useful for real-time applications where its speed advantage matters.

Measurement Considerations

Successful impulse response measurement requires attention to numerous practical factors. Background noise sets the floor below which decay cannot be measured, requiring either quiet conditions or sufficient source level. The source must provide adequate low-frequency output to excite room modes, while high-frequency content enables fine temporal resolution. Measurement duration must exceed the room's reverberation time to capture complete decay.

Positioning follows standardized protocols for comparable results. ISO 3382 specifies minimum distances between sources, receivers, and room boundaries. Multiple positions sample the room's spatial variation, with averaging providing representative parameters. Different applications (occupied versus unoccupied, stage versus audience area) may require separate measurement campaigns.

RT60 Definition and Measurement

RT60 (also written T60 or simply RT) defines the time required for sound energy to decay by 60 dB after the source stops. This 60 dB range corresponds to roughly one-millionth of the original energy, representing the decay from a loud sound to the threshold of audibility in a quiet room.

Direct measurement of 60 dB decay requires very high source levels or very low background noise. Practical measurements therefore evaluate portions of the decay curve and extrapolate. T20 measures the decay from -5 dB to -25 dB below the initial level, then multiplies by three to estimate the full 60 dB decay. T30 uses the -5 dB to -35 dB range, multiplied by two. The -5 dB starting point avoids the direct sound and early reflections, focusing on the reverberant decay.

Schroeder's backward integration method derives the decay curve from the impulse response by integrating energy from the end of the response backward in time. This approach provides smoother decay curves than traditional interrupted noise methods, revealing deviations from ideal exponential decay that indicate acoustic anomalies.

Frequency Dependence

Reverberation time varies with frequency because absorption coefficients of room surfaces are frequency-dependent. Most absorptive materials work more effectively at high frequencies, causing rooms to typically have longer reverberation at low frequencies. Measurement standards specify evaluation in octave or third-octave bands from 125 Hz to 4 kHz, with extensions to 63 Hz and 8 kHz for complete characterization.

Balanced reverberation across frequency contributes to natural sound quality. Excessive low-frequency reverberation creates boomy, muddy acoustics, while insufficient low-frequency decay sounds thin. Acoustic design aims for flat or gently rising reverberation time from high to low frequencies, with the slope depending on the room's intended use.

Optimal Reverberation Times

Different activities require different reverberation times, and extensive research has established optimal ranges for various applications. Concert halls for symphonic music benefit from reverberation times of 1.8 to 2.2 seconds, providing the blend and warmth that enhance orchestral sound. Chamber music venues work well at 1.4 to 1.8 seconds, balancing clarity with support for acoustic instruments.

Speech-focused spaces require shorter reverberation. Lecture halls and classrooms target 0.6 to 0.8 seconds to maintain intelligibility. Conference rooms typically aim for 0.4 to 0.6 seconds. Recording studios for speech may be as short as 0.2 to 0.3 seconds to capture clean, dry recordings. These guidelines scale with room volume, with larger rooms tolerating longer reverberation while maintaining clarity.

Perceptual Significance

In occupied rooms with audiences, absorption increases and RT60 decreases, but EDT often decreases more dramatically because audience absorption primarily affects early reflections from seating areas. A concert hall with RT60 of 2.0 seconds might have EDT of 1.6 seconds when occupied. The lower EDT value better predicts the perceived reverberance that listeners experience.

The ratio between EDT and RT60 indicates decay linearity. In well-diffused rooms with uniform decay, EDT approximately equals RT60. When EDT significantly exceeds RT60, strong early reflections create an initial decay faster than the reverberant tail. When EDT falls well below RT60, coupled spaces or non-uniform absorption create complex decay behavior.

Design Implications

Acoustic designers manipulate EDT independently from RT60 through careful placement of absorptive and reflective surfaces. Early reflection patterns from nearby surfaces determine EDT, while total room absorption controls RT60. A recording studio might have low EDT for clarity while maintaining modest RT60 from distant surfaces. A concert hall might use overhead reflectors to enhance EDT while relying on volume and diffusion for appropriate RT60.

Clarity C80

C80 compares sound energy arriving within the first 80 milliseconds to energy arriving later, expressed in decibels. The 80 ms integration time approximates the ear's temporal integration for music perception. Positive C80 values indicate early energy dominance (high clarity), while negative values indicate late energy dominance (low clarity).

Concert halls typically aim for C80 between -2 dB and +2 dB, balancing the clarity needed for rhythmic precision against the reverberant blend that enhances tonal richness. Values above +4 dB may sound overly dry, while values below -4 dB compromise articulation. Different musical styles have different preferences within this range, with baroque music generally favoring higher clarity than romantic repertoire.

Clarity C50

C50 uses a 50 ms integration time, appropriate for speech perception where shorter syllables require faster temporal resolution. Speech intelligibility benefits from high C50 values, typically +2 dB to +6 dB in well-designed lecture spaces. C50 correlates strongly with speech transmission index and provides a simpler measure when full STI measurement is impractical.

Definition D50

Definition D50 (also called Deutlichkeit) expresses the same early-to-total ratio as a percentage rather than a decibel value. D50 equals the ratio of energy within the first 50 ms to total energy, multiplied by 100. Values above 50% indicate good speech clarity, with excellent intelligibility corresponding to D50 above 70%.

Center Time

Center time (Ts) calculates the temporal center of gravity of the impulse response's energy. Lower values indicate that energy arrives predominantly early, correlating with high clarity. Center time provides a single-number characterization of the energy distribution without requiring selection of an arbitrary integration time. Values below 60 ms indicate high clarity suitable for speech, while values above 100 ms suggest reverberant conditions better suited to organ music or choral works.

Measurement Principle

Speech carries information through amplitude modulations at rates from about 0.5 Hz to 16 Hz. The STI method measures how faithfully these modulations transmit from source to receiver. The modulation transfer function (MTF) compares modulation depth at the receiver to modulation depth at the source for each modulation frequency and carrier frequency combination.

Reverberation reduces modulation depth because reverberant energy fills in the gaps between speech syllables. Background noise adds unmodulated energy that also reduces apparent modulation. Both effects degrade the MTF and reduce STI. The measurement combines MTF values across seven octave bands (125 Hz to 8 kHz) and 14 modulation frequencies using a weighted averaging scheme derived from speech perception research.

STI Measurement Methods

Direct STI measurement uses specialized test signals consisting of modulated noise bands. The equipment measures modulation reduction in each frequency band and calculates STI according to standardized algorithms. This approach captures the combined effects of room acoustics, background noise, and any sound reinforcement system.

Indirect STI calculation derives the index from the measured impulse response and specified background noise level. This approach separates room acoustics from other degradation factors and enables prediction of STI for different noise conditions. However, it cannot capture sound system nonlinearities or distortion that direct measurement includes.

STI Interpretation

STI ranges from 0 (completely unintelligible) to 1 (perfect transmission). Standardized quality categories guide interpretation:

• Excellent: STI above 0.75 - Nearly all speech understood with ease
• Good: STI 0.60 to 0.75 - Most speech understood with attention
• Fair: STI 0.45 to 0.60 - Speech understood with concentration and repetition
• Poor: STI 0.30 to 0.45 - Speech difficult to understand
• Bad: STI below 0.30 - Speech essentially unintelligible

Building codes and standards increasingly specify minimum STI values. Classrooms typically require STI above 0.60, public address systems above 0.50, and emergency voice communication systems above 0.45 under alarm conditions. These requirements drive acoustic design decisions and sound system specifications.

RASTI and STIPa

Rapid speech transmission index (RASTI) was a simplified version using only two frequency bands, now largely obsolete. STIPa (STI for public address systems) uses a compressed test signal enabling faster measurement while maintaining correlation with full STI. STIPa has become the practical standard for field measurement of installed sound systems, providing quick verification that systems meet intelligibility requirements.

Measurement Approach

Dual-channel FFT analysis computes the transfer function as the complex ratio of output spectrum to input spectrum. The measurement requires simultaneous capture of both signals, either through direct electrical connection to the source signal or by using a reference microphone near the source. Phase information preserves timing relationships between frequencies.

Coherence, computed alongside the transfer function, indicates measurement reliability at each frequency. A coherence of 1.0 means the output perfectly relates to the input; lower values indicate noise, nonlinearity, or time variance. Frequencies with low coherence should be interpreted cautiously, and the condition causing poor coherence investigated.

Room Frequency Response

Room transfer functions typically show significant variation with frequency, particularly at low frequencies where room modes dominate. Peaks and dips of 20 dB or more are common, causing dramatic coloration of reproduced sound. The response varies substantially with position, with some locations exhibiting severe modal problems while others happen to fall at favorable positions.

Spatial averaging of transfer function measurements provides a more representative characterization. The average smooths position-dependent variations while preserving consistent room characteristics. Design of sound reinforcement systems and room equalization typically targets spatially averaged response rather than optimizing for any single position.

System Identification

Transfer function measurement enables identification of installed sound systems including room effects. Measuring from electrical input to acoustic output reveals the combined response of amplifiers, loudspeakers, and room. This data guides equalization to compensate for frequency response deviations, flatten coverage, and optimize system performance for the specific acoustic environment.

Mode Types

Axial modes involve reflections between two parallel surfaces, with resonant frequencies determined by the distance between surfaces and the speed of sound. A room dimension of 5 meters creates axial modes at 34.3 Hz, 68.6 Hz, 102.9 Hz, and higher harmonics. Each pair of parallel surfaces creates its own series of axial modes.

Tangential modes involve reflections from four surfaces (such as floor, ceiling, and two walls), creating more complex pressure patterns. Oblique modes involve all six surfaces, with the most complex distribution but lowest energy per mode. The total number of modes increases rapidly with frequency, eventually becoming too dense for individual modes to be distinguishable.

Modal Measurement

Modal measurement involves exciting the room with sine waves or broadband signals and measuring the spatial pressure distribution. Swept sine measurements with high frequency resolution reveal individual mode frequencies and their quality factors (sharpness of resonance). Multiple microphone positions map the spatial pressure patterns, identifying nodes (pressure minima) and antinodes (pressure maxima).

Modern measurement systems can compute modal parameters from impulse response data using curve-fitting algorithms. These techniques identify mode frequencies, damping factors, and mode shapes from measurements at multiple positions. The results validate room acoustic models and guide placement of absorption to address problematic modes.

Modal Density and Transition

Modal density increases with frequency cubed, meaning modes become progressively closer together. Below approximately three times the lowest mode frequency, individual modes are clearly separated and dominate the acoustic behavior. Above this region, modes overlap and statistical acoustic behavior emerges. The transition frequency, sometimes called the Schroeder frequency, marks this boundary and typically falls between 100 Hz and 300 Hz for typical rooms.

Room proportions affect modal distribution. Some dimension ratios create coincident modes where multiple modes share the same frequency, causing severe resonance. Preferred room ratios distribute modes evenly across frequency, minimizing peaks and gaps in the response. Design guidelines specify favorable ratios for critical listening rooms and recording studios.

Measurement Standards

Laboratory measurement of absorption coefficients follows standardized procedures ensuring comparable results between facilities. ISO 354 and ASTM C423 specify reverberation chamber methods using large sample areas (typically 10 to 12 square meters). The absorption coefficient equals the difference in room absorption with and without the sample, divided by sample area.

Reverberation chamber measurements can yield absorption coefficients exceeding 1.0, which seems physically impossible since a coefficient of 1.0 implies perfect absorption. This apparent anomaly results from edge diffraction effects and serves as a reminder that laboratory coefficients are effective values for prediction rather than true physical absorption percentages.

In-Situ Measurement

Field measurement of installed materials uses impedance tube methods or reflectometry techniques. Impedance tubes measure absorption of small samples under controlled conditions, useful for material development and quality control. Reflectometry analyzes reflections from surfaces to infer absorption, enabling non-destructive characterization of installed treatments.

In-situ absorption often differs from laboratory values due to mounting conditions, size effects, and contamination. Periodic verification ensures that installed treatments maintain expected performance, particularly in critical facilities where acoustic specifications must be maintained over time.

Frequency Dependence

Absorption varies significantly with frequency, and different materials excel in different frequency ranges. Porous absorbers work well at mid and high frequencies where viscous losses within the material dissipate sound energy. Membrane absorbers target low frequencies through resonant damping. Helmholtz resonators provide narrowband low-frequency absorption at tuned frequencies.

Absorption data is typically reported in octave bands from 125 Hz to 4 kHz. The noise reduction coefficient (NRC) averages the 250 Hz, 500 Hz, 1 kHz, and 2 kHz values, providing a single-number rating for general comparisons. However, frequency-dependent behavior matters for design, and reliance on NRC alone can lead to inadequate low-frequency treatment.

Impedance Tube Method

Impedance tubes (also called standing wave tubes or Kundt's tubes) measure normal-incidence absorption and impedance of small samples. A loudspeaker at one end generates sound that travels down the tube and reflects from the sample at the other end. The interference between incident and reflected waves creates a standing wave pattern whose characteristics reveal the sample's acoustic properties.

Transfer function methods using two microphones have replaced older standing wave ratio techniques. The complex transfer function between microphone positions enables calculation of complex reflection coefficient, from which impedance, absorption, and phase derive. Measurements span frequencies from a lower limit set by tube diameter to an upper limit set by microphone spacing.

Surface Impedance and Boundary Conditions

Surface impedance determines how room boundaries affect sound propagation and is essential input for wave-based room acoustic modeling. Real surfaces have complex, frequency-dependent impedance that varies with angle of incidence. Locally reactive surfaces have impedance independent of incident angle, simplifying analysis. Extended reaction surfaces (typical of porous materials backed by air gaps) have angle-dependent impedance requiring more complex treatment.

Modeling Approach

BEM discretizes room boundaries into elements, each with specified acoustic impedance. The method solves for pressure and velocity at element centers, then computes the sound field throughout the room. Because BEM only meshes boundaries rather than the full volume, it handles large spaces more efficiently than finite element methods while accurately capturing wave phenomena.

Input data includes room geometry (typically from CAD models or measured surveys) and boundary impedance (from material databases or impedance measurements). Source and receiver positions correspond to measurement locations, enabling validation against measured data.

Applications

BEM excels at predicting low-frequency room behavior where modes dominate. Design of recording studios, listening rooms, and home theaters benefits from BEM analysis to identify modal problems before construction. Optimization routines can search for room proportions, absorption placement, and treatment configurations that minimize frequency response variation.

Comparison between BEM predictions and measurements validates models and identifies discrepancies requiring investigation. Agreement confirms that geometry and boundary conditions accurately represent the actual room; disagreement prompts examination of potential sources including construction deviations, unexpected absorption sources, or modeling simplifications that prove inadequate.

Limitations

BEM computational requirements increase with frequency because element size must remain small relative to wavelength. Practical limitations typically restrict BEM to frequencies below 200 to 500 Hz, depending on room size and available computing resources. For higher frequencies, geometric acoustics methods using ray tracing or image sources provide efficient alternatives. Hybrid approaches use BEM for low frequencies and geometric methods for high frequencies, capturing the full audio bandwidth.

Measurement Microphones

Calibrated measurement microphones provide the known, consistent response essential for accurate room measurement. Free-field microphones have flat on-axis response and are oriented toward the sound source. Diffuse-field microphones have flat response when averaged over all angles, appropriate for reverberant field measurements. Typical sensitivities range from 12 to 50 mV/Pa, with noise floors below 20 dB(A) for adequate dynamic range.

Omnidirectional capsules capture sound from all directions equally, appropriate for most room acoustic measurements. Specialized measurements may use directional patterns to isolate specific reflections or characterize directional room response. Arrays of multiple microphones enable spatial analysis and sound field visualization.

Sound Sources

Omnidirectional sound sources distribute energy uniformly in all directions, ensuring that room response reflects actual acoustic behavior rather than source directivity. Dodecahedron loudspeakers with drivers on all faces approximate omnidirectional radiation. Balloon bursts and starter pistols provide impulsive sources for interrupted decay measurements. Subwoofers supplement main sources when low-frequency room modes require characterization.

Source output level must exceed background noise by sufficient margin to measure the full decay range. For RT60 measurement, 45 dB signal-to-noise ratio enables T30 evaluation; 65 dB enables full T60 measurement. More powerful sources or lower background noise extends measurement capability in challenging environments.

Analysis Systems

Modern room acoustic measurement uses software running on laptops or tablets with calibrated audio interfaces. Dedicated applications generate test signals, acquire responses, perform analysis, and present results. Key capabilities include impulse response measurement via swept sine, computation of standard room acoustic parameters, transfer function analysis, and report generation.

Multi-channel systems measure multiple positions simultaneously, dramatically accelerating spatial surveys. Automated turntables enable directivity measurements of loudspeakers and measurement of directional room response. Integration with room modeling software enables comparison between predicted and measured results.

ISO 3382 Series

ISO 3382 defines methods for measuring room acoustic parameters in performance spaces, ordinary rooms, and open offices. Part 1 covers performance spaces (concert halls, theaters, auditoriums) with detailed specifications for source and receiver positions, parameter calculations, and reporting. Part 2 addresses ordinary rooms (classrooms, conference rooms) with simplified procedures appropriate for smaller spaces. Part 3 specifies open plan office measurements including spatial decay parameters.

The standard ensures that measurements made by different teams at different times yield comparable results. Compliance with ISO 3382 is often required for acoustic consultancy reports, building certification, and research publications.

IEC 60268-16

IEC 60268-16 defines speech transmission index measurement methods and equipment requirements. The standard specifies test signals, measurement procedures, and calculation algorithms ensuring consistent STI results across different measurement systems. Conformance testing verifies that STI meters provide accurate results.

Other Relevant Standards

ISO 354 specifies reverberation chamber measurement of absorption coefficients. ISO 10534 covers impedance tube measurements. ASTM standards provide North American alternatives to ISO standards for many measurements. Building codes reference these standards when specifying acoustic requirements, making standards compliance essential for demonstrating regulatory conformance.

Pre-Measurement Planning

Successful measurement campaigns begin with clear objectives and careful planning. Define which parameters are needed, what accuracy is required, and how results will be used. Review relevant standards for position requirements and measurement conditions. Survey the space to identify potential sources of background noise, access limitations, and safety considerations.

Prepare a measurement position plan showing source and receiver locations that satisfy standard requirements while being practically achievable. Consider whether measurements represent the occupied or unoccupied condition, as significant differences exist. Schedule measurements during periods of low background noise if possible.

Equipment Setup

Verify calibration of all measurement equipment before beginning. Position sources and receivers at specified heights, typically 1.2 to 1.5 meters representing seated listener ear height. Ensure adequate separation from boundaries as standards require. Verify signal levels provide sufficient margin above background noise without overloading any component in the measurement chain.

Document equipment configuration, calibration status, and any deviations from standard procedures. This documentation enables future measurements to replicate conditions and supports interpretation of results.

Data Acquisition

Perform measurements systematically, working through planned positions while monitoring data quality. Check coherence (for transfer function measurements) or signal-to-noise ratio (for impulse response measurements) to verify adequate measurement conditions. Repeat measurements that show questionable quality.

Record background noise levels at representative positions. Document any unusual conditions such as HVAC operation, external noise events, or temporary installations that might affect results. Photograph source and receiver positions for documentation and future reference.

Analysis and Reporting

Process raw data to extract parameters specified in measurement objectives. Apply appropriate averaging (spatial, frequency band, or both) as standards require. Compare results against criteria or specifications when applicable. Identify any anomalies requiring investigation or explanation.

Report results clearly, including measurement conditions, equipment, procedures, and any deviations from standards. Graphical presentation of frequency-dependent parameters aids interpretation. Uncertainty estimates, where available, indicate confidence in results. Archive raw data to enable future reanalysis if questions arise.

Architectural Acoustics

Room acoustic measurement supports the entire lifecycle of architectural projects. Pre-design measurements characterize existing conditions and inform requirements. Design-phase measurements verify that mockups and test installations achieve targets. Commissioning measurements confirm completed spaces meet specifications. Post-occupancy evaluation identifies issues requiring remediation and documents achieved performance.

Concert hall and theater design relies extensively on measurement to validate acoustic models and refine details. Multiple measurement campaigns during construction track progress and catch problems early. The extensive databases of measurements from successful venues guide design of new facilities.

Sound System Design

Room measurements inform sound system design by characterizing the acoustic environment systems must operate within. Reverberation time and STI measurements establish achievable intelligibility limits. Transfer function measurements reveal frequency response variations requiring equalization. Coverage measurements guide loudspeaker placement and aiming.

System commissioning verifies that installed systems achieve design targets. STI measurements confirm speech intelligibility meets requirements. Coverage measurements demonstrate uniform sound distribution. Delay settings optimize coherence between distributed loudspeakers. The measurement data documents system performance for client acceptance.

Recording and Broadcast Facilities

Critical listening environments require detailed acoustic measurement to verify design achievement. Control room measurements confirm low-frequency response flatness and symmetric stereo imaging. Reverberation time measurements verify that decay characteristics match design targets. Modal measurements identify resonances requiring treatment.

Recording spaces are characterized to document their acoustic signatures. This data aids selection of appropriate spaces for different recording projects and enables electronic simulation of room acoustics in post-production.

Building Certification

Green building certification systems increasingly include acoustic criteria. LEED, WELL, and similar programs specify reverberation time limits and background noise levels for various space types. Measurement demonstrates compliance with these criteria, supporting certification applications. Schools, offices, and healthcare facilities particularly benefit from acoustic certification requirements that ensure appropriate acoustic conditions.