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Frequencies and rhythms
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Rates and rhythms with their value, units, scope and source.
68 rows.
| name | value | units | scope | class | source |
|---|---|---|---|---|---|
| f₁ | ≈ 7.83 | Hz | Earth–ionosphere cavity, global; observed peaks are wide | OBSERVED-REPLICATED | Schumann (1952) predicted; Balser & Wagner (1960), Nature 188:638–641 |
| f₁ range | 7.5–8.1 (mode 1); station/component specific (e.g. 7.2–8.2 B_EW; 7.6–7.9 B_NS) | Hz | per-station, per-component — not a planetary constant | OBSERVED-REPLICATED (as station data) | station ELF records; see NA-06 |
| f₁ global diurnal constant | — | — | — | NOT-MEASURED | no single global figure found by this chapter's search; only station-specific ranges |
| f_ideal | ≈ 7.49 | Hz | ideal lossless cavity: c ÷ Earth circumference (≈3.00×10⁵ km/s ÷ 4.0075×10⁴ km) | MODELED | textbook derivation |
| B_SR | picotesla (pT) range | T | ELF background amplitudes | OBSERVED-REPLICATED | Balser & Wagner (1960), Nature 188:638–641 |
| SR → human physiology | — | — | ambient (pT) field strengths | NOT-MEASURED | no pre-registered, independently replicated dose–response found by this chapter's search |
| f_α | 8–13 (≈10 dominant) | Hz | human posterior cortex; relaxed wakefulness; eyes closed | OBSERVED-REPLICATED | Berger (1929), Über das Elektrenkephalogramm des Menschen; IFCN definition |
| f_WBV | 4–8 vertical; 1–2 horizontal; 4–16 hand/arm | Hz | human whole-body mechanical vibration sensitivity | OBSERVED-REPLICATED | ISO 2631-1:1997 |
| A4 | 440 ± 0.5 | Hz | Western concert pitch, by convention, at ~20 °C | OBSERVED-REPLICATED (as a standard, not a natural constant) | ISO 16:1975, Acoustics — Standard tuning frequency |
| f_SR1 | ≈7.83 | Hz | fundamental Schumann mode, Earth–ionosphere cavity, global | OBSERVED-REPLICATED | Schumann (1952) prediction; experimental confirmation 1954 |
| f_SR1 range | NOT-MEASURED | Hz | diurnal/solar variation reported as ~7.5–8.1 Hz in secondary sources only; no primary-source range extracted — recorded empty rather than laundered | NOT-MEASURED | — |
| f_heart, Suncus etruscus (2 g) | resting 835 ± 107; max 1093 ± 235; peak single 1511 | min⁻¹ | 22 °C ambient, smallest mammal | OBSERVED-REPLICATED | Jürgens et al. (1996) JEB 199:2579–2584 |
| f_heart, blue whale (~70 t) | dive 4–8 (min 2); surface 25–37; predicted resting 15 | bpm | foraging dive cycle, ≤184 m, ≤16.5 min | OBSERVED-REPLICATED | Goldbogen et al. (2019) PNAS 116:25329–25332 |
| EEG band bounds | delta 0.5–1.5 → 2.5–6; alpha 7.5–8.5 → 11–14; gamma 20–37 → 38–100 | Hz | 135 resting-state EEG studies | OBSERVED-CONTESTED (bands real; bounds conventional) | Newson (2018), Sapien Labs, survey of 135 studies; Buzsáki & Draguhn (2004) Science 304:1926–1929 |
| τ_circadian (human, free-running) | 24.18 (earlier reports 13–65, median 25.2 — artefactual) | h | controlled lighting, young + older adults | OBSERVED-REPLICATED | Czeisler et al. (1999) Science 284:2177–2181, doi:10.1126/science.284.5423.2177 |
| Kinesin velocity | ~800 | nm·s⁻¹ | low load, saturating ATP, in vitro, buffer; clamp range F=1–8 pN, [ATP]=1 µM–2 mM | OBSERVED-REPLICATED | Visscher, Schnitzer & Block (1999) Nature 400:184–189, doi:10.1038/22146 |
| F₁-ATPase rotation | ~130 rev·s⁻¹; 120° = ~90° + ~30° substeps, two ~1 ms reactions | rev·s⁻¹ / degrees | saturating ATP; mechanism holds to nM ATP | OBSERVED-REPLICATED | Yasuda et al. (2001) Nature 410:898–904, doi:10.1038/35073513; Noji et al. (1997) Nature 386:299–302 |
| RNAP elongation | E. coli 40–80; HeLa Pol II 30–100 (median 60) | nt·s⁻¹ | E. coli 37 °C; HeLa in vivo | OBSERVED-REPLICATED | BioNumbers BNID 104900/104902/108488; 111027 |
| Ribosome elongation | ~20 | aa·s⁻¹ | E. coli, 37 °C | OBSERVED-REPLICATED | BioNumbers BNID 100059/105067/108490 |
| f_Schumann | 7.83; harmonics 14.1, 20.3, 26.3, 32.5 (ideal theory predicts ~11) | Hz | Earth–ionosphere cavity, global | OBSERVED-REPLICATED | Schumann (1952) Z. Naturforsch. A 7:149–154, doi:10.1515/zna-1952-0202; Balser & Wagner (1960) Nature 188:638–641 |
| Q_Schumann | 3.5, 4.5, 6.2, 7.7, 8.2 (modes 1–5); width ~20% | dimensionless | Earth–ionosphere cavity | OBSERVED-REPLICATED | Nickolaenko & Hayakawa (2002), Kluwer |
| B_Schumann | ~1 (vs Earth static 30,000–50,000) | pT | at the surface | OBSERVED-REPLICATED | Nickolaenko & Hayakawa (2002) |
| f₁ cantilever | f₁ ≈ 0.162·(t/L²)·√(E/ρ) | Hz | uniform rectangular cantilever, mode 1, small deflection | MODELED (Euler–Bernoulli assumptions) | Blevins, Formulas for Natural Frequency and Mode Shape (1979) |
| Q of soft biological tissue | NOT-MEASURED | — | — | NOT-MEASURED | No sourced value obtained; Wakeling, Nigg & Rozitis (2002) J. Appl. Physiol. observe damping increases with muscle activity |
| Brainwave entrainment efficacy | NOT-MEASURED | — | — | NOT-MEASURED | Not assessed in this chapter |
| ω_F1 | ~130 | rev/s | F₁, saturating ATP; 120° = 90° + 30° substeps | OBSERVED-REPLICATED | Yasuda et al. 2001, Nature 410:898–904 |
| r_rib,ec | ~20 (range 4–22) | aa/s | E. coli, growth-rate dependent | OBSERVED-REPLICATED | BNID 100059, 105067, 108490 |
| r_rib,euk | 3–10 (yeast, 30 °C); ~6 (mouse ES) | aa/s | eukaryote | OBSERVED-REPLICATED | BNID 107871, 107952 |
| r_RNAP,ec | 40–80 | nt/s | E. coli | OBSERVED-REPLICATED | BNID 104900, 104902, 108488 |
| r_RNAP,mam | 50–100 elongation vs ~6 average-across-gene | nt/s | mammalian — do not conflate | OBSERVED-REPLICATED | BNID 105566/105113/100662; BNID 100661 |
| f_Schumann | 7.83 (harmonics ~14.3, 20.8, 27.3, 33.8) | Hz | Earth–ionosphere cavity fundamental | OBSERVED-REPLICATED | Schumann 1952 (prediction); Schumann & König 1954 (confirmation); Balser & Wagner 1960 |
| c_air | 343.2 | m/s | 20 °C; √(γRT/M), γ=1.400 | MODELED | Computed in-chapter |
| c_air (0 °C) | 331.3 | m/s | 0 °C, same formula | MODELED | Computed in-chapter |
| α (measured) | 1 kHz: 4.7 / 10 kHz: 160 | dB/km | 20 °C, 101.325 kPa, 50% RH | OBSERVED-REPLICATED (tertiary reproduction) | NPL Kaye & Laby tables, as reproduced by Frontier Labs |
| α humidity shape | non-monotonic: peak 280 at 20% RH; 190 → 240 → 95 dB/km at 10 → 30 → 90% RH | dB/km | 10 kHz, 20 °C | OBSERVED-REPLICATED (tertiary reproduction) | as above |
| α below 1 kHz | — | dB/km | infrasound / low audio band | NOT-MEASURED | not fetched in this pass |
| f_5min | ~3,300 (≈3.3 mHz, ~5 min period) | μHz | solar p-mode power peak | OBSERVED-REPLICATED | Leighton, Noyes & Simon 1962, ApJ 135:474; Deubner 1975, A&A 44:371 |
| f_beat | 23 (low visc) / 11 (high visc) | Hz | same cells, 37 °C; low-visc buffer vs ~0.14 Pa·s analogue | OBSERVED-REPLICATED | Smith et al. 2009 |
| f_beat (Saggiorato) | ~20 | Hz | human sperm, 37 °C, buffer ~0.7 mPa·s, tethered, n = 35 | OBSERVED-REPLICATED | Saggiorato et al. 2017, Nat Commun 8:1415, DOI 10.1038/s41467-017-01462-y |
| SL_blue | 189 ± 3 | dB re 1 µPa @ 1 m, 25–29 Hz | calibrated bottom-moored hydrophones, W. Antarctic Peninsula | OBSERVED-REPLICATED | Širović, Hildebrand & Wiggins 2007, JASA 122(2):1208–1215 |
| SL_fin | 189 ± 4 | dB re 1 µPa @ 1 m, 15–28 Hz | as above | OBSERVED-REPLICATED | Širović et al. 2007 |
| SL_sperm | 236 max; 235 representative (8 events 226–234) | dB re 1 µPa rms (on-axis) | Physeter, large-aperture array, 14 h, Bleik Canyon | OBSERVED-SINGLE | Møhl et al. 2003, JASA 114(2):1143–1154 |
| SL_sperm,offaxis | 170–180 (classical) vs 202–223 (large-aperture) vs 236 (on-axis) | dB re 1 µPa | the same animal — the spread is aspect angle, not disagreement | OBSERVED-REPLICATED | Møhl et al. 2003 (reviewing Backus & Schevill 1966 etc.) |
| SL_sperm,air-equiv | 173 | dB SPL re 20 µPa | 235 dB re 1 µPa rms converted by the source authors | MODELED | Møhl et al. 2003 |
| t_click / f_c | ~100 µs / 15 kHz (cBW_rms 4.1 kHz) | s / Hz | on-axis p1 pulse | OBSERVED-SINGLE | Møhl et al. 2003 |
| α(100 Hz) | 0.0012 → r₁₀dB 8,333 | dB/km → km | Thorp, published table | OBSERVED-REPLICATED | TU Delft OCW reader ch.3 |
| α(1 kHz) | 0.07 → r₁₀dB 143 | dB/km → km | Thorp, published table | OBSERVED-REPLICATED | as above |
| α(10 kHz) | 1.2 → r₁₀dB 8.3 | dB/km → km | Thorp, published table | OBSERVED-REPLICATED | as above |
| α(20 Hz) | ~4.8 × 10⁻⁵ → r₁₀dB ~2.1 × 10⁵ | dB/km → km | computed in-chapter, Thorp extrapolated below its fitting range | MODELED | Computed in-chapter; formula per Thorp 1967 |
| α_air,2kHz | ≈ 9.9 dB/km ≈ 1.14 × 10⁻³ m⁻¹ | dB/km; m⁻¹ | air at 2 kHz, 20 °C, 50% RH, 101.325 kPa — the condition is part of the number | MODELED (ISO 9613-1 evaluated in-chapter) | ISO 9613-1 (the standard, not the course reader); implementation checked against ISO 9613-2 Table 2 |
| f_range | ~9–11 to 212 | kHz | dominant (peak) frequency of the strongest call component, across species. Floor is species-dependent, set by E. maculatum. The 212 kHz endpoint is a CF carrier | OBSERVED-REPLICATED (as a range) / span attribution NOT-CONFIRMED | Thiagavel et al. 2017, Sci Rep 7:828. Fenton et al. 1998's confirmed subject is the 20–60 kHz assemblage result, not the full span |
| f_mode | 20–60 | kHz | aerial-feeding assemblages: Canada, Mexico, Brazil, Zimbabwe | OBSERVED-REPLICATED | Fenton et al. 1998, Can J Zool 76(6):1174–1182 |
| f_Cloeotis | 212 | kHz | Cloeotis percivali carrier — chain-flagged (M22) | OBSERVED-CONTESTED / NOT-CONFIRMED | Thiagavel et al. 2017 citing Bell & Fenton 1984, Behav Ecol Sociobiol 15:109–114 (primary not read in this pass) |
| f_Euderma | 9–12 (also reported ~10.5, ~12.7) | kHz | Euderma maculatum dominant/peak frequency — real spread across sources. This species is what sets the f_range floor | OBSERVED-CONTESTED | Fullard & Dawson 1997, J Exp Biol 200:129–137; ~10.5 in Thiagavel et al. 2017 |
| rate_buzz | >160 (up to ~170) | calls/s | terminal buzz repetition rate | OBSERVED-REPLICATED | Elemans et al. 2011, Science 333(6051):1885–8; Moss & Surlykke 2010 |
| f_muscle | up to 160; 200 in one case | Hz | anterior cricothyroid, Myotis daubentonii, positive work in cyclic contraction | OBSERVED-REPLICATED | Elemans et al. 2011 |
| f_fovea | 83.0–84.5 | kHz | R. ferrumequinum inferior colliculus, overrepresented best frequencies | OBSERVED-REPLICATED | Schuller & Pollak 1979, J Comp Physiol 132:47–54 |
| SD_echo | 110 (= 0.17% of F_ref) | Hz | Hipposideros armiger (a hipposiderid — NOT a rhinolophid/horseshoe bat), in-flight DSC precision. An emission-control statistic: how tightly the bat stabilises F_echo. It is NOT a measured resolution requirement of the bat's receiver, and the source does not claim it is | OBSERVED-REPLICATED | Schoeppler, Schnitzler & Denzinger 2018, Sci Rep 8:4598 |
| band_DSC | 0.1–0.2% of F_ref (≈83–166 Hz at F_ref = 83 kHz) | % of F_ref | rhinolophids and P. parnellii — the band: precision within which F_echo is held around F_ref. A different quantity from offset_DSC below | OBSERVED-REPLICATED | Schoeppler et al. 2018, Sci Rep 8:4598 |
| offset_DSC | ~150–200 | Hz (F_ref above F_rest) | R. ferrumequinum, R. euryale, P. parnellii, in flight — the offset, not the band | OBSERVED-REPLICATED | Schoeppler et al. 2018 |
| Δf_emit | ~2.4 | kHz (lowering) | bat at v = 5 m/s, f_r = f_e(c+v)/(c−v), F_ref = 83 kHz | MODELED | Computed in-chapter |
| SL_open | ~130, up to and beyond 140 | dB SPL re 20 µPa @ 0.1 m | open-space aerial-hawking bats | OBSERVED-REPLICATED | Surlykke & Kalko 2008, PLoS ONE 3:e2036; Jakobsen et al. 2013 |
| SL_whisper | up to 110 (not ~70) | dB SPL re 20 µPa @ 0.1 m | 'whispering' bats | OBSERVED-REPLICATED | Jakobsen et al. 2013 |
| rate_pulse,flight | 19.7 ± 2.7 (range 15.3–25.8) | pulses/s | Rhogeessa io, in flight (non-buzz) | OBSERVED-REPLICATED | Voigt & Lewanzik 2012 |
| f_click,B.trigona | up to 4,500 | clicks/s | Bertholdia trigona — chain-flagged | NOT-CONFIRMED | tertiary source citing Corcoran et al. 2009; primary not read in this pass |
| alpha_atm@212kHz | — | dB/m | absorption at Cloeotis's carrier | NOT-MEASURED | not sourced in this pass |
| N_beats,mammal | 7.3 ± 5.6 × 10⁸ (CV ≈ 77%) | beats/lifetime | 15 mammal species, excluding humans. Provenance, per Levine's own Fig. 1 caption — 'Most coordinates represent average values (4–6)': refs 4–6 are Spector, Handbook of Biological Data (1956); Encyclopaedia Britannica (1971); and White et al. (1938). Species lifespan/HR coordinates not independently traced | OBSERVED-CONTESTED (a loose 'invariant', on averaged and untraced coordinates) | Levine 1997, J Am Coll Cardiol 30:1104–1106 |
| DR_hearing | 10⁶ pressure / 10¹² intensity (0→120 dB SPL; 20 µPa → 20 Pa) | dimensionless | The ratio follows from the dB definition; the endpoints do not. 0 dB SPL = the 20 µPa reference level, anchored near 1 kHz — not 'the threshold of hearing'. 120 dB upper endpoint = a convention, no source carried | MODELED (the ratio) / NOT-MEASURED (both endpoints) | Computed in-chapter from the 20 µPa reference level; no primary carried for either endpoint |
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