Sound Pressure and Sound Quality Analysis

The problem it solves

The A-weighted level answers only how loud a sound is. Sounds of equal level — a low hum or a high hiss — are perceived very differently: the first is dull but tolerable, the second irritating. Most noise complaints about appliances, vehicles and motors are not about exceeding a level but about harsh high-frequency content or noticeable modulation — sound quality problems.

The traditional approach uses a sound level meter for levels, an octave analyzer for spectra and separate sound quality software for psychoacoustic indicators: three systems and three data sets that are hard to align in time and cannot analyze many channels at once. Integrated in the T8 vibration and acoustic system, the module computes sound level statistics, octave spectra, FFT spectra and Zwicker sound quality for eight channels at every refresh, answering four questions in one measurement: how loud, what content, how pleasant and whether tones are present.

Functions

Screen layout

1. Statistics table (top): all 16 indicators for each channel, updated at every refresh.
2. Time waveform (middle): sound pressure (Pa) of the selected channel against time in ms.
3. Octave view (lower left): 1/3 octave Z/A/C, 1/1, 1/12, specific loudness and excitation level.
4. Spectrum view (lower right): FFT magnitude in dB, FFT phase or the Fast (125 ms) level history.

The left panel selects the channels to analyze and the analysis channel used for tone detection; below it, the tone and peak list shows the main peak frequencies, levels and tone marks.

Sound quality of appliances and electromechanical products

For air conditioners, refrigerators, washing machines, vacuum cleaners, motors and pumps, loudness decides whether a limit is exceeded, sharpness whether the sound is harsh, and roughness or fluctuation strength whether there is annoying modulation. Quantifying these in development, with octave and specific loudness spectra to find the frequency source of harsh components, gives a direct basis for acoustic improvement.

Occupational noise exposure

Workplace assessment concerns not only the instantaneous level but the accumulated exposure over eight hours. The module gives the noise dose (%) and the eight-hour time-weighted average level (TWA) directly for comparison with occupational limits.

Tonality of fans and wind turbines

Fan and wind turbine noise rules (such as IEC 61400-11) require a decision on audible tones, which strongly increase the risk of complaints. The module searches spectral peaks, calculates tone prominence and marks components above 6 dB as tones without manual reading.

Workshop and environmental noise statistics

Fluctuating noise, such as intermittent machines or traffic, is badly described by instantaneous levels. The module calculates statistics over the whole period (maximum and minimum level, sound exposure level SEL) and, with the octave spectrum, identifies the spectral composition and main contributing bands.

Speech communication environments

Control rooms, command centers and cabins need speech intelligibility. The articulation index (AI, 0 to 1) quantifies how clearly speech is transmitted against the current background, guiding noise control targets and public address design.

Training and demonstration

With the supplied example data, all functions — stepped octave spectra, Bark specific loudness, Fast level history and tone detection — can be demonstrated without a sound calibrator.

Sound pressure level and frequency weighting

Lp = 20 · lg(p / 20 µPa) [dB]

The reference of 20 µPa is the threshold of hearing at 1 kHz. A and C weightings correct the spectrum band by band according to IEC 61672: A-weighting models the ear's low sensitivity at low frequencies (used for environmental and occupational noise); C-weighting is flat and keeps low-frequency energy (used for impulse and peak evaluation).

Equivalent level, exposure level and statistics

The equivalent continuous level Leq is the energy average of the squared sound pressure over the analysis period. The sound exposure level normalizes the total energy to one second, SEL = Leq + 10 · lg(T), for fair comparison of events of different duration. Kurtosis, crest factor (peak / RMS), impulse factor (peak / mean absolute value) and form factor (RMS / mean absolute value) are dimensionless waveform statistics with typical values for sine and random noise; clear deviations indicate impacts or modulation.

Octave spectra (IEC 61260)

The range from 20 Hz to 16 kHz is divided into standard bands: 10 bands for 1/1 octave, 30 bands for 1/3 octave and the corresponding finer division for 1/12 octave. Each band level is the energy sum of the FFT lines in the band:

L_band = 10 · lg(Σ p² / p0²) [dB]

Bands are drawn as steps from lower edge to upper edge, as on acoustic instruments. The 1/3-octave view supports Z, A and C weighting, with corrections at each band center. Empty bands are clamped to 0 dB so the curve does not drop abnormally.

Fast time-weighted level history (IEC 61672)

Env(i) = α · x²(i) + (1 − α) · Env(i − 1), α = 1 − exp(−1 / (0.125 · Fs))

The Fast setting of a sound level meter is a first-order exponential average of the instantaneous power with a 125 ms time constant. The averaging state is kept between data blocks, so long histories have no jump at the start of each block, consistent with a real sound level meter.

Zwicker loudness and critical bands (ISO 532-1)

The cochlea acts like a filter bank: 24 critical bands (Bark scale) each sense the energy in their range. Loudness is calculated in four steps:

Ln = 40 + 10 · log2 N (for N ≥ 1 sone)

Each doubling of loudness adds 10 phon — the essential difference between perception and physical decibels.

Sharpness, roughness and fluctuation strength

Sharpness is the weighted average of specific loudness over critical band rate; bands above 15.8 Bark are weighted increasingly, emphasizing harsh high-frequency content, in acum. Roughness and fluctuation strength describe rapid variation of the envelope: the signal is rectified and low-pass filtered to extract the envelope, and the modulation depth and frequency are estimated in the 20–200 Hz range (roughness, with maximum sensitivity at 70 Hz modulation) and the 0.5–20 Hz range (fluctuation strength, maximum at 4 Hz), then converted with psychoacoustic weighting curves.

Articulation index (ANSI S3.5)

The 15 one-third-octave bands above 200 Hz are weighted by their importance for speech intelligibility. The signal-to-noise ratio of each band between −15 and +30 dB is mapped linearly to 0–1, and the weighted sum is the articulation index. The closer AI is to 1, the easier speech is to understand.

Tone prominence (IEC 61400-11 basis)

Local maxima in the FFT magnitude spectrum are candidate peaks. For each, the difference between its level and the mean noise level in its critical band (prominence) is calculated. Peaks more than 6 dB prominent are audible tones and marked in the tone list, which also gives the peak frequency (Hz) and level (dB) of up to six main peaks.

Performance

All indicators are calculated per channel at every refresh. The windowed FFT of the main analysis chain is reused rather than computed twice, and data-heavy views such as 1/12 octave are calculated on demand, so continuous refreshing is possible with many channels for online monitoring.

Preparation

1. Microphones: 0.5–1 m from the source, away from air outlets and reflecting surfaces; with several channels keep the distance to the source similar.
2. Calibration: calibrate with a sound calibrator (for example 94 dB at 1 kHz) and check that the equivalent level in the table matches after refresh.
3. Acquisition: a sampling rate of at least 51.2 kHz for a 20 kHz analysis bandwidth; choose the number of points for the required 1/12-octave low-frequency resolution.

Procedure

Recommended views

Channel 1, near field of a fan prototype:

• Equivalent level 83.9 dB and sound exposure level 89.1 dB.
• Kurtosis 1.49 and crest factor 2.31, both typical of steady noise, so the signal contains no clear impacts.
• No exposure conclusion is drawn from this example: dose/TWA settings, representative measurement periods and daily task durations are not established.
• Loudness 51.63 sone (about 97 phon) with a high sharpness of 2.872 acum, indicating a sharp sound. The specific loudness and 1/3-octave spectra show strong contributions between 1 and 4 kHz, so improvement should target the air path and blade design in that range.
• The tone list shows main peaks at 125 Hz, 315 Hz and others; peaks marked as tones are more than 6 dB prominent and their mechanical or electromagnetic sources should be investigated first.

The reading order — overall level (Leq), character (kurtosis, crest factor), perception (loudness, sharpness) and frequency location (octave, specific loudness, tone list) — leads from data to improvement measures in four steps.