Causal limits and optimal allocation for passive frequency-selective hearing protection
Abstract
Passive Helmholtz-resonator earplugs aim to attenuate hazardous noise while keeping speech audible; the air volume of an ear-sized shell is finite, and we treat it as the resource a design spends. For a vented bore transparent at zero frequency and loaded by reactive side branches, causality fixes a conserved integral of transmission loss. We derive it in device variables, add viscous and flanking constraints, and allocate the budget by hazard-weighted water-filling with a continuous speech-cost price. The audio-band budget B_ad = (20/ln10) pi^2 V / 2cS is set by the ratio of total cavity volume V to bore area S; occluding plugs are exempt. The f^2 price signal favours frequencies well above the source peak. Replacing strict transparency by a speech-cost price gives an exchange rate of about 1.3 dB of protection per decibel of speech cost under the present model, with the budget setting where it saturates. Across three form factors, low-frequency-selective designs stay near a decibel while hazard-matched mid/high-frequency designs reach twelve. The binding variables are bore area and speech allowance, not resonator count.
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BibTeX
@misc{hwang2026causal,
title = {{Causal limits and optimal allocation for passive frequency-selective hearing protection}},
author = {Geonhwi Hwang and Jaewoo Lee and Hyunjun Kim and Hyeonwoo Na},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22395},
eprint = {2609.22395},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22395},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Causal limits and optimal allocation for passive frequency-selective hearing protection
AU - Geonhwi Hwang
AU - Jaewoo Lee
AU - Hyunjun Kim
AU - Hyeonwoo Na
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22395
UR - https://arxiv.org/abs/2609.22395
AB - Passive Helmholtz-resonator earplugs aim to attenuate hazardous noise while keeping speech audible; the air volume of an ear-sized shell is finite, and we treat it as the resource a design spends. For a vented bore transparent at zero frequency and loaded by reactive side branches, causality fixes a conserved integral of transmission loss. We derive it in device variables, add viscous and flanking constraints, and allocate the budget by hazard-weighted water-filling with a continuous speech-cost price. The audio-band budget B_ad = (20/ln10) pi^2 V / 2cS is set by the ratio of total cavity volume V to bore area S; occluding plugs are exempt. The f^2 price signal favours frequencies well above the source peak. Replacing strict transparency by a speech-cost price gives an exchange rate of about 1.3 dB of protection per decibel of speech cost under the present model, with the budget setting where it saturates. Across three form factors, low-frequency-selective designs stay near a decibel while hazard-matched mid/high-frequency designs reach twelve. The binding variables are bore area and speech allowance, not resonator count.
ER -