A Note on the Resonance Frequency Equation of Microperforated Panel Sound Absorber
Bibliographic record
Abstract
Microperforated panel, MPP, can be considered as a multi or N-holes Helmholtz resonator. It is a light, clean and tunable sound absorber, for which a first modeling was established by Maa in 1975. It is a resonator in sub-millimeter size of diameter (0.5–1) mm, to provide enough acoustic resistance and low acoustic mass reactance which are necessary for wide-band sound absorber. The characteristic property of such a resonator is its ability to absorb sound waves of a particular frequency, the so-called resonant frequency. In practical and engineering applications, for prefabricated microperforated panel, it is important to determine the resonance frequency as precisely as possible, especially if the panel will be used as a sound absorber at a certain frequency. There is high deviation between the exact resonance frequency value of single MPP absorber which can be obtained from the peak of calculated absorption curve by Maa’s equation and that value which can be calculated by the classical N-holes Helmholtz resonance frequency equation. A proposed modified and simplified equation for calculating the resonance frequency of single MPP sound absorber of hole diameter (0.5–1) mm, which derived from absorption equation of Maa, is introduced. The new proposed equation gave good agreement and little deviation, maximum deviation was about 5 Hz over frequency range from 50 Hz to 1000 Hz, from the exact value of resonance frequency.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".