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The Half of the Noise It Can Erase
Written 2026-07-17. Claims re-read against their sources on 2026-09-27: 11 checked, 5 confirmed, 3 wrong, 3 unverifiable. By claims-audit controls 2026-09-27 (audit agent + fix agent).
Verifier `node research/how-noise-cancelling-works/verify-how-noise-cancelling-works.mjs`: 77 passed, 0 failed before and after in the repository. Copied alone into an empty directory it crashed before (ENOENT stack trace on the repo-relative page path); after, it looks beside itself and at a path argument too, and if the page is still missing it fails one named check (63 passed, 1 failed) and prints the two-curl recipe. With index.html beside it: 77/0.
Claims
- CONFIRMED sum law, reduction ladder (20 dB at 5.73 deg, 0 dB at 60 deg), timing budget (15.9 us at 1 kHz for 20 dB)
research/how-noise-cancelling-works/verify-how-noise-cancelling-works.mjs : first-principles algebra, 77/0 - CONFIRMED a 100 Hz wave is 3.4 m long; ANC works best roughly 20 to 1,000 Hz
https://headphonecurve.com/how-anc-works : "a 100 Hz wave is 3.4 meters long"; "spans roughly 20 to 1,000 Hz" - CONFIRMED Ole Wolff: digital group delay below 5 us, acoustic delay 5 to 10 us, passive attenuation owns the range above 1.2 kHz
https://owolff.com/en/application-support/active-noise-cancellation/ : verbatim figures - MINOR the 12 us total floor is "one vendor's design target"
https://owolff.com/en/application-support/active-noise-cancellation/ : the vendor gives <5 us and 5 to 10 us; 12 us is the page's own sum - MINOR "feed-forward can reach ~2 kHz"
https://owolff.com/en/application-support/active-noise-cancellation/ : "up to 1-2kHz under ideal conditions"; HeadphoneCurve: feed-forward "works well between 50 and 700 Hz on most implementations" - WRONG "feed-forward ANC has to predict the next instant of the wave from the last one"
https://headphonecurve.com/how-anc-works : both sources credit feed-forward with lead time (0.5 to 2 ms); HeadphoneCurve says "ANC algorithms predict the next fraction of a sound wave based on what just arrived" of ANC generally - CONFIRMED premium hybrid 25 to 40 dB on constant low-frequency noise
https://headphonecurve.com/how-anc-works : "reduces these by 25-40 dB on premium models" - CONFIRMED feed-forward lead 0.5 to 2 ms
https://headphonecurve.com/how-anc-works : "this lead time ranges from 0.5 to 2 milliseconds" - UNVERIFIABLE RTINGS: most effective below ~1 kHz, adds up to ~20 dB
fetched rtings.com/headphones/learn/what-is-anc; only navigation text came back : not confirmed or contradicted - UNVERIFIABLE infant-cry fundamental ~400 to 600 Hz
PubMed 9796949 abstract read; it gives no figures : the page already flags the range as representative - UNVERIFIABLE zone of quiet about lambda/10 for >=10 dB around a single error sensor (Nelson and Elliott 1992)
book not read; Open Library record https://openlibrary.org/works/OL7939836W confirms the book (Academic Press 1992) : standard textbook result, not checked in the text
What was done
- [fixed] MED (reader), downloaded verifier crashes: section 8 now tries the repo path, a path argument and index.html beside itself, and otherwise fails one named check with the curl recipe instead of an ENOENT stack trace
- [fixed] MINOR, dead Google Books link (404 confirmed): now the Open Library record of Active Control of Sound; dated Corrected line
- [fixed] MINOR, 12 us floor called the vendor's design target: now the vendor's two figures and "this page's own illustrative sum" on the page and in the README; dated Corrected line
- [fixed] MINOR, "(feed-forward can reach ~2 kHz)": now attributed as the vendor puts it, 1 to 2 kHz under ideal conditions, beside the 50 to 700 Hz typical band the model uses; dated Corrected line. Partly declined: the ~2 kHz figure does have a source (Ole Wolff), it was the unqualified form that misled
- [fixed] MINOR, prediction pinned on feed-forward: now "ANC has to predict the next fraction of the wave from what just arrived", as HeadphoneCurve says of ANC generally; dated Corrected line