# Why you can hear Nová Osmička from Beethovenova 1847 Sound propagation study, 7 August 2026, 20:00–22:00 CEST. Stage 49.6768614 N, 18.3597356 E → flat 49.6687125 N, 18.3525188 E. **1045.4 m at 209.89°.** **Short answer:** your hypothesis is wrong, but only about *which* height matters. The venue really is 6.6 m higher than your building's ground — that part is right — but that 6.6 m is worth **+0.3 dB**. Your fifth floor is worth **+5.7 dB**, and the reason you hear only the low end is that 4 kHz arrives **70 dB weaker than 63 Hz**, of which 23 dB is pure atmospheric absorption and only 15 dB is the buildings. --- ## 1. Terrain elevations and the profile between them Source: **ČÚZK DMR 5G**, the national lidar terrain model, stated vertical accuracy **0.18 m** in open terrain (0.30 m forested), vertical datum Bpv. Read through the ArcGIS `identify` endpoint and, independently, through `exportImage` as a float32 raster resampled bilinearly. The two routes agree to **0.016 m**. | | terrain, m ASL | |---|---| | Hlavní stage | **298.28** | | Beethovenova 1847, ground | **291.68** | | **difference** | **+6.60 m, venue higher** | Recommended error bar **± 0.3 m**. Every one of the 13 datasets queried puts the source at or above the receiver; none reverses the sign. ČÚZK DMR 4G — an older, separately processed product — reproduces the difference to **8 cm** (+6.686 m). The coarse global DEMs appear to disagree (EU-DEM +1.29 m, SRTM30 +1.0 m, Copernicus GLO-30 +1.54 m), and that disagreement is fully explained rather than being error: they are *surface* models, and your point sits under 26.4 m of building. Box-averaging ČÚZK's own data to a simulated 30 m DSM cell predicts **+1.56 m**; Copernicus measured **+1.54 m**. Agreement to 3 cm. The coarse DEMs corroborate ČÚZK, they don't contradict it. Datum mixing was checked with PROJ grid transforms and is worth **under 1.5 cm** here — a non-issue. **Profile along the path** (401 samples, figure 1): terrain leaves the stage on a small terrace at 298.4 m, drops off that terrace at ~150 m, then runs across the open Ostravice floodplain at 287–292 m for roughly 700 m, bottoming at **287.30 m in the Ostravice channel at 627 m**, before rising to 291.68 m at your building. The river crossing is 42 m of water at 624 m along, in a channel incised 2.9 m below its banks. ## 2. Is there line of sight? **Yes to the terrain, and very nearly yes to the buildings.** This is not a shadowed path. Taking the PA acoustic centre 4 m above stage terrain (302.3 m ASL) and your ear at 291.68 + 17 = **308.68 m ASL**, the straight sight line clears the *bare terrain* by **14–18 m across the entire middle 700 m of the path**. The Ostravice sits 19 m below the line. Terrain plays no blocking role whatsoever. Against the *surface* model (DMP 1G, buildings and vegetation at 1 m resolution) only **12 of 401 samples** are blocked, all in the last 170 m: | along path | what it is | top, m ASL | intrusion above sight line | |---|---|---|---| | 76 m | factory-hall corner at the venue | 303.9 | +1.1 m | | 883 m | apartment row | 310.1 | +2.4 m | | **949 m** | **8-storey block, 25.4 m tall** | **316.7** | **+8.6 m** ← dominant | OSM independently tags that block `building:levels = 8` → 25.5 m estimated; the lidar measures **25.4 m**. The resulting path-length difference over the two-edge route is only **δ = 0.42 m** (single dominant edge) to 0.68 m (double). That is the whole story: **Fresnel-zone check at the dominant edge** (d₁ = 949 m, d₂ = 96 m): | frequency | λ | 1st Fresnel radius r₁ | obstruction / r₁ | Fresnel number N = 2δ/λ | diffraction loss | |---|---|---|---|---|---| | 60 Hz | 5.73 m | 6.68 m | 1.29 | 0.15 | ~10 dB | | 120 Hz | 2.87 m | 4.72 m | 1.82 | 0.29 | ~12 dB | | 4 kHz | 0.086 m | 0.82 m | 10.5 | 9.8 | ~26 dB | At 60 Hz the obstacle is barely larger than the Fresnel zone it has to block. At 4 kHz it is ten times larger. Same building, same geometry, entirely different outcome. ## 3. What actually dominates — ranked, with numbers Computed by counterfactual: re-running the geometry with one factor changed at a time. | rank | factor | worth at 63 Hz | how it was obtained | |---|---|---|---| | 1 | **Atmospheric absorption's frequency dependence** | **23.4 dB** of 4 kHz-vs-63 Hz discrimination | ISO 9613-1 at 22.3 °C / 69 % / 983.8 hPa: 0.084 dB/km at 63 Hz vs 22.5 dB/km at 4 kHz | | 2 | **Source spectrum** | **24.4 dB** | measured 170-concert FOH spectrum, +4 dB hip-hop sub adjustment | | 3 | **Low-frequency diffraction** | **14.9 dB** | barrier costs 63 Hz 14.8 dB but 4 kHz 29.7 dB | | 4 | **Your floor height** | **+5.7 dB** (and +8.3 dB at 4 kHz) | 5th floor vs ground floor, same everything else | | 5 | **Refraction (downwind + inversion)** | **+2 to +5 dB** vs a neutral atmosphere | CONCAWE K4 category 6, argued to the low end for this elevated geometry | | 6 | **Terrain elevation difference** | **+0.3 dB** | flattening the 6.6 m changes the barrier loss by 0.3 dB | Items 1–3 answer *why only the bass*. Items 4–6 answer *why at all*, and item 4 is the one that matters. **Why the terrain contributes so little:** the dominant barrier sits at 949 m, i.e. **91 % of the way to you**. Raising the *source* by 6.6 m lifts the sight line at that barrier by only 6.6 × 96/1045 = **0.6 m**. Raising the *receiver* by 15 m lifts it by 15 × 949/1045 = **13.6 m**. Your height has a ~10× longer lever arm. Elevation near the source is nearly wasted; elevation near the receiver is not. **Meteorology** (ICON-D2, figure 4). Sunset was 20:18, so the set began exactly at the evening transition; the boundary layer collapses from 1285 m at 17:00 to 220 m at 22:00. | hour | 2 m→80 m gradient | class | wind 10 m | angle to path | net dc_eff/dz | ray radius | |---|---|---|---|---|---|---| | 20:00 | −0.90 K/100 m | stable lapse | 1.8 m/s from 49° | 19° | +0.0204 s⁻¹ | 16.9 km | | 21:00 | −0.26 K/100 m | stable lapse | 1.1 m/s from 45° | 15° | +0.0239 s⁻¹ | 14.4 km | | 22:00 | **+0.26 K/100 m** | **inversion** | 1.3 m/s from 32° | **2°** | +0.0349 s⁻¹ | 9.9 km | Two things worth stating plainly: - **You are downwind, essentially exactly.** The back-azimuth from your flat to the stage is 29.9°; at 22:00 the wind came *from* 32°. That is 2° off perfect alignment. Refraction is downward for the whole evening. - **It is not primarily an inversion — it's wind shear.** At 20:00 the temperature term is *negative* (−0.0052 s⁻¹, still a lapse); the wind-shear term (+0.0256 s⁻¹) is what makes the net gradient positive. A true inversion only appears at 22:00. **A correction to the premise in your brief:** the "inversion adds 5–15 dB" figure is a category error that propagates widely. Those numbers are *downwind-minus-upwind spreads*, and most of the spread is the upwind shadow-zone **loss**, not a downwind **gain**. Measured against a neutral atmosphere, CONCAWE's data give only **+2 to +7 dB** at 1 km at these frequencies, and for a 4 m source / 17 m receiver — where the neutral-case ground-interference dip is already shallow — the low end is the defensible one. What refraction really buys you is that it removes the possibility of a shadow zone: upwind, the geometric shadow would begin at ~1045 m, right at your window. ### Your hypothesis, tested > "the venue sits at a higher altitude than me, that's why I hear it" **The premise is right and the conclusion is wrong.** The venue *is* 6.6 ± 0.3 m higher than your building's ground — that is real and measured. But it buys **0.3 dB**. And it is more than cancelled by your own height: your ear at 308.68 m ASL is **6.4 m above the stage PA**, not below it. You are not listening uphill. You are listening slightly *downhill*, from a fifth floor that lifts you over the only two obstacles on the path. Replace "the venue is higher" with **"I am high enough to see over the last row of blocks, and bass barely notices what's left"** and the physics agrees with you. ## 4. Level budget at your window Source assumption: **L_Aeq,FOH = 100 dB at 25 m**, octave spectrum from Støfringsdal's 170-concert survey (digitised from WHO 2020 Fig. 2), plus +4 dB at 63 Hz / +2 dB at 125 Hz for hip-hop sub content. Modelled as an omnidirectional point source of that strength with an off-axis directivity correction applied. | band | L_w | A_div | A_atm | A_bar | directivity | **arriving** | dB(A) | night ambient | hearing threshold | indoors, windows shut | |---|---|---|---|---|---|---|---|---|---|---| | 63 | 149.8 | −71.4 | −0.09 | −14.8 | −3 | **60.5** | 34.3 | 55 | 37.5 | 47.5 | | 125 | 143.5 | −71.4 | −0.33 | −16.4 | −5 | **50.3** | 34.2 | 44 | 22.1 | 30.3 | | 250 | 138.3 | −71.4 | −1.16 | −18.5 | −8 | **39.3** | 30.7 | 35 | 11.4 | 14.3 | | 500 | 136.3 | −71.4 | −3.08 | −21.3 | −8 | **32.5** | 29.3 | 29 | 4.4 | 4.5 | | 1 k | 134.4 | −71.4 | −5.74 | −24.3 | −8 | **24.9** | 24.9 | 25 | 2.4 | −5.1 | | 2 k | 129.8 | −71.4 | −9.96 | −27.1 | −8 | **13.3** | 14.5 | 22 | −1.3 | −18.7 | | 4 k | 125.4 | −71.4 | −23.49 | −29.7 | −10 | **−9.2** | −8.2 | 20 | −5.4 | −43.2 | **Totals: L_Zeq 60.9 dB · L_Aeq 38.9 dB(A) · L_Ceq 60.2 dB(C) · C−A = 21.3 dB.** Residential night ambient for comparison: ~34.5 dB(A) (NR-25 design floor). This reproduces exactly what you describe: - At **63 Hz** the signal arrives **23 dB above the hearing threshold** outdoors and still **10 dB above it indoors with the windows closed**. Clearly audible, and it is the *only* band with a double-digit indoor margin. - At **4 kHz** it arrives **below the threshold of hearing**. Not quiet — absent. - In A-weighted terms the whole event is only **+4.4 dB over ambient**, which is why an A-weighted measurement would call this a non-event while your ears call it obvious. **C−A of 21 dB** is the signature of a bass-only arrival. ## 5. What I assumed, and where the error bars are **Measured, not assumed:** both terrain elevations; the 401-point terrain and surface profile; building heights along the corridor; the river crossing; all meteorology; the ISO 9613-1 absorption coefficients. **Assumed, in descending order of how much it could move the answer:** 1. **PA directivity toward you — ±15 dB, the largest single uncertainty.** I do not know which way the stage faces, and cardioid subs versus conventional subs is alone worth 15–20 dB at 63 Hz. I used −3 dB at 63 Hz (conventional stack, off-axis) and −8 to −10 dB in the mids and highs. If the stage faces you and the subs are conventional, add ~3 dB; if it faces away with cardioid subs, subtract up to 17 dB at 63 Hz. 2. **Source level, ±3 dB.** 100 dB(A) at FOH is the canonical operating point, not a measurement of this event. Note that FOH is 20–40 m from the stage, not 10 m — the "at 10 m" framing in the brief would put L_w about 8 dB lower for the same FOH reading. 3. **Barrier method, +0/−4 dB at 63 Hz.** Four methods were run and they bracket 63 Hz at **10.7–20.8 dB** (single knife edge / Epstein-Peterson / Deygout+Causebrook / ISO 9613-2 §7.4 double). I adopted the mean, 14.8 dB. A naive uncorrected Deygout gives 23.4 dB and over-counts grazing sub-edges — I rejected it. 4. **Source height 4 m**, receiver ear height **+17 m** (your 3 m/storey + 2 m, taken as given). If "5th floor" means the 6th storey in the Czech sense, add 3 m and roughly 1 dB. 5. **Ground effect folded into the barrier term** rather than computed separately. ISO 9613-2's C₂ = 20 form embeds ground reflection, and with a 25 m barrier at 949 m the terms are not cleanly separable. The corridor is mixed ground (G_s 0.22 / G_m 0.40 / G_r 0.51; 37 % acoustically hard). 6. **Ambient floor is a design criterion, not a measurement.** NR-25 is a standard curve, not a survey of your street. The key point survives regardless: an ambient of 33–37 dB(A) carries **51–55 dB in the 63 Hz octave**, about 20 dB more than the A-weighted figure suggests. 7. **Facade insulation** from published measurements of a lightweight dwelling (13 dB at 63 Hz), not your building. **Honest single-night point-prediction uncertainty for outdoor propagation at 1 km is ±8–10 dB rms.** Every number above should be read with that in mind. The *relative* frequency structure — the 70 dB gap between 63 Hz and 4 kHz — is far more robust than any absolute level, because it comes from terms that are physics (absorption, wavelength) rather than estimates. ## 6. Where data was unavailable or coarse - **OSM building heights are effectively absent here.** Of 295 buildings in the corridor, **zero** carry an explicit `height` tag; 129 carry `building:levels` (converted at 3.0 m/level + 1.5 m roof); **166 have neither**. The obstruction profile therefore rests on ČÚZK DMP 1G lidar, not OSM. Where both exist they agree well (25.5 m tagged vs 25.4 m measured on the dominant block). - **ČÚZK's `getSamples` endpoint returns HTTP 403.** Profiles were built from `exportImage` rasters instead and spot-checked against `identify` at 12 points (max difference 0.035 m). - **`exportImage` silently expands a non-square bbox** to match the requested image aspect ratio. The returned extent must be read back from `f=json`; assuming the requested bbox produces a ~0.9 m elevation error. - **Open-Meteo pressure levels are unusable here.** The 1000 hPa geopotential height is 140–172 m ASL, i.e. *below* the 298 m terrain, so those fields are below-ground extrapolations. The 80/120/180 m above-ground levels were used instead. 80 m is the lowest Open-Meteo exposes, and NWP models under-resolve nocturnal surface inversions, so the reported gradient is a **lower bound** on the real near-surface stability. - **Model spread is real:** at 20:00 ICON-D2 says stable lapse while GFS says inversion. Both give downward refraction; they disagree on the mechanism. - **ECMWF IFS returns nulls** for every above-ground height level; MeteoFrance AROME has no coverage here (HTTP 400). Copernicus GLO-30 was pulled from the AWS Open Data COG (no free no-auth *point* API exists); OpenTopography's endpoint requires an API key and was not used. - **The source spectrum is a figure digitisation**, not a published table — Støfringsdal (2018) via WHO (2020) Fig. 2. It re-integrates to 100.0 dB(A) against its stated normalisation, so I trust it, but it should be cited as a digitisation. - **ISO 9613-2 is being used outside its stated validity.** It is specified to 1000 m with mean heights under 30 m, and is not designed for successive rows of apartment blocks. Our path is 1045 m. Stated accuracy ±3 dB inside the range; treat it as worse here. - **The adversarial verification pass did not run.** The workflow was stopped after the data-acquisition and reference-grounding phases to wrap up. The core numbers were nonetheless cross-checked independently: the terrain profile was computed twice by different agents and agrees to **0.001 m**, and the ISO 9613-1 coefficients were implemented twice and agree to four decimal places. - **A legal note that reframes the context:** Czech hygiene noise limits (NV 272/2011 Sb.) do **not** legally apply to outdoor music — since 2015, § 30 of zák. 258/2000 Sb. excludes it from the definition of "hluk". The binding instrument is Frýdek-Místek's OZV č. 4/2026, which sets noční klid at 22:00–06:00 and contains no dB figure at all. 7 August 2026 is a Friday and is *not* on the venue's exemption list, which is very likely why the main set ends at exactly 22:00. ## Files ``` sound-propagation/ ├── REPORT.md ├── figures/ │ ├── 1_cross_section.png terrain + buildings + sight line + 60 Hz Fresnel ellipsoid │ ├── 2_plan_view.png hillshade map, corridor, Ostravice, buildings by height │ ├── 3_spl_by_band.png arriving SPL vs ambient and hearing threshold + loss ledger │ ├── 4_temperature_profile.png vertical T profile, refraction terms, downwind geometry │ └── 5_interactive_map.html folium: clickable path, per-sample clearance, building tooltips └── data/ ├── profile_cuzk.json 401-point DMR 5G terrain + DMP 1G surface profile ├── buildings_osm.json 295 buildings with resolved heights and tagging provenance ├── weather.json 6 models, hourly, incl. derived gradients and downwind components ├── dem_crosscheck.json 13 datasets, accuracies, datums, spread reconciliation ├── corridor_context.json river crossing, landcover, ISO 9613-2 ground factors ├── hydro_landuse.json Ostravice/Morávka geometry └── level_budget.json the per-band table above ``` Data sources: ČÚZK DMR 5G / DMR 4G / DMP 1G (ArcGIS ImageServer) · OpenStreetMap via Overpass · Open-Meteo (ICON-D2, ICON-EU, ECMWF IFS, GFS) · OpenTopoData · Copernicus GLO-30 (AWS Open Data) · ISO 9613-1:1993 · ISO 9613-2:1996 · ISO 226:2023 · IEC 61672-1:2013 · CONCAWE 4/81.