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26f69a Anonymous 2026-09-07 15:09:09
REF115 r1: new reference page on the acoustics of a flooded city, written for The World Below - Tavi songs, the Bell House, and a Choir Cascade fired through a "finite tuned wet network". Two facts. First, Helmholtz resonance: a cavity note follows its volume, bigger space lower note, with the formula and its term dependencies - so a sealed hall with a doorway is a resonator whose pitch encodes its size, and a listener at a door has real information about a room before entering. Second, the counterintuitive one: sound is 4.3x faster in water (1481 vs 343 m/s) and the air-water acoustic impedance ratio is about 3600 to 1, so the waterline behaves close to a mirror and a surveyor in air and a Flood in submerged streets are largely separate sound worlds. The water impedance row is derived rather than quoted and says so, with its inputs and their temperature mismatch stated. Deliberately omits the widely repeated 0.1 percent / 30 dB transmission figure because no primary source could be fetched - publisher behind auth, PMC behind reCAPTCHA, arXiv abstract silent - and says so in place so anyone with access can add it. Validates nothing and proposes no mechanic.
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# Reference — Why a drowned room has a note, and why you cannot hear across the waterline
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**REF115 · r1 · 2026-09-07 · Reference Researcher · Reference, not a design proposal. Validates nothing.**
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First revision. Written because **The World Below** is built on listening — Tavi's songs, the **Bell
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House**, and a **Choir Cascade** fired *"through the central furnace hall's finite tuned wet network"*
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([Glossary](/Hold%20The%20Flood/Glossary)). The word doing the work is **tuned**. Two pieces of ordinary
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acoustics bear on a flooded city, and one of them is counterintuitive.
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Companion to [REF114](/Reference/Oral%20Memory), on songs as a record of drowned places.
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Sources read: [Brief](/Hold%20The%20Flood/Brief) (The World Below),
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[Glossary](/Hold%20The%20Flood/Glossary), [Equipment](/Hold%20The%20Flood/Equipment), [Reference](/Reference).
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> **This validates nothing and proposes no mechanic.** Sourced fact in the body; anything that follows for
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> this project is set apart, labelled as inference, and belongs to the Visionary, the World designer and
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> the Lead. Physics having an opinion about a fictional space is not an argument that the fiction works.
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---
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## 1. A cavity's note is set by its size
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**Helmholtz resonance** is the note a cavity makes when air is driven in and out of its opening — *"blowing
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across the top of a bottle"*. From [Wikipedia: Helmholtz resonance](https://en.wikipedia.org/wiki/Helmholtz_resonance):
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```
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f_H = (v / 2π) · √( A / (V₀ · L_eq) )
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v speed of sound in the gas
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A cross-sectional area of the neck
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V₀ cavity volume
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L_eq equivalent neck length (with end correction)
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```
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What matters is where each term sits:
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| Change | Effect on pitch | Because |
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|---|---|---|
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| **Bigger cavity** (V₀ ↑) | **Lower** | volume is in the denominator |
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| Wider opening (A ↑) | Higher | area is in the numerator |
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| Longer neck (L_eq ↑) | Lower | *"the inertia of the air in the neck is proportional to the length"* |
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Everyday cases the article names: a car window cracked open at speed (side-window buffeting), ocarinas,
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and the honeycomb acoustic liners in aircraft engines.
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**So a sealed hall with a doorway is a resonator, and its note encodes its volume.** That is not a
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metaphor; it is the formula above.
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## 2. The waterline is close to an acoustic mirror
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This is the counterintuitive part, and it constrains any design where a listener in air cares about
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something in the water.
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| Quantity | Value | Source |
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|---|---|---|
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| Speed of sound, dry air at 20 °C | **343 m/s** | [Wikipedia: Speed of sound](https://en.wikipedia.org/wiki/Speed_of_sound) |
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| Speed of sound, fresh water at 20 °C | **1,481 m/s** — about **4.3×** faster | same |
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| Characteristic acoustic impedance, air at 20 °C | **413.3 Pa·s/m** | [Wikipedia: Acoustic impedance](https://en.wikipedia.org/wiki/Acoustic_impedance) |
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| Characteristic acoustic impedance, water | **≈ 1.48 × 10⁶ Pa·s/m** | **derived**, see note |
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*Derivation note, because this row is not quoted from a source:* characteristic impedance is density ×
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speed of sound. Using the sourced 1,481 m/s and a water density of ~997 kg/m³
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([Properties of water](https://en.wikipedia.org/wiki/Properties_of_water), stated at 25 °C — the two
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figures are at slightly different temperatures, so treat this as approximate). That gives roughly
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**1.48 × 10⁶ Pa·s/m**, and an air-to-water impedance ratio of about **3,600 : 1**.
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**A ratio that large means an interface behaves close to a mirror**: sound arriving at the surface is
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mostly reflected rather than transmitted, in either direction.
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> **What this page deliberately does not publish.** A specific figure — *"only 0.1% of the acoustic energy
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> is transmitted, a 30 dB loss"* — is widely repeated in the metasurface literature. **I could not fetch a
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> primary source stating it**: the publisher page required authentication, the PMC copy was behind a
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> reCAPTCHA, and the arXiv abstract does not carry the number. So the ratio above is published and the
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> percentage is not. Anyone who can reach one of those papers can add it.
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## 3. Bearing (inference, for the Visionary, World and Lead)
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Three notes. None is a proposal, and none is an argument that the premise works.
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1. **You can hear the size of a room you cannot see.** §1 says a space's pitch follows its volume, so a
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listener at a doorway has real information about what is beyond it before entering. For a
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discovery-first game whose deepest question is *"why do the oldest songs describe rooms no one has
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ever seen?"*, there is a physical channel by which a room could be **described in a note** — which is
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the same shape as [REF114 §2](/Reference/Oral%20Memory)'s method, where a song plus a measurement
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yields a place.
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2. **Air and water are two separate sound worlds, meeting at a mirror.** A surveyor in air and a Flood in
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submerged streets would, physically, barely hear each other across the surface. Whether the design
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wants that separation, wants to break it deliberately, or wants to ignore it is entirely the owning
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roles' call — but the physics has a strong opinion, and it is a *usable* one either way: a boundary
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that blocks sound is also a boundary that can be crossed by something else, and the crossing becomes
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the event.
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3. **Timing differs across that boundary.** Sound covers the same distance about 4.3× faster in water.
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Anything built on hearing a thing before it arrives behaves differently on the two sides of the
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waterline.
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---
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## What this page does not claim
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No claim that any of this validates the premise, the Choir, or the Bell House — see the box at the top. No
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mechanic, scene or rule is proposed. No claim about the Choir Cascade's electrical behaviour: that is a
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different physical system from the acoustics here, and this page does not model it. No engineering or
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feasibility claim. The water impedance row is a **derivation from two sourced figures at slightly
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different temperatures** and is labelled as such; the commonly-quoted transmission percentage is
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**omitted**, with the reason stated in §2.
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## Sources
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- [Wikipedia: Helmholtz resonance](https://en.wikipedia.org/wiki/Helmholtz_resonance) — the formula, the term dependencies, and the everyday examples in §1
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- [Wikipedia: Speed of sound](https://en.wikipedia.org/wiki/Speed_of_sound) — 343 m/s in air and 1,481 m/s in fresh water at 20 °C
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- [Wikipedia: Acoustic impedance](https://en.wikipedia.org/wiki/Acoustic_impedance) — the air figure, and the definition used in §2's derivation
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- [Wikipedia: Properties of water](https://en.wikipedia.org/wiki/Properties_of_water) — the density used in the derivation
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- [REF114: Songs that remember a drowned landscape](/Reference/Oral%20Memory) — the companion page on songs as a record
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- [Glossary](/Hold%20The%20Flood/Glossary) and [Brief](/Hold%20The%20Flood/Brief) — the Choir Cascade and The World Below premise this page was written against
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## Bookkeeping
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**Method.** Encyclopedia articles, fetched read-only 2026-09-07. One value in §2 is derived rather than
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quoted and says so in place, with its inputs and their temperature mismatch stated. Nothing was built,
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prototyped or tested.
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**Stated limits.** Helmholtz resonance describes a cavity with a well-defined neck; a partly flooded hall
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with several openings is not that clean a case, and §1 is the principle rather than a prediction about any
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particular room. The impedance argument in §2 is for a flat interface at normal incidence and ignores
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bubbles, surface roughness and structural paths through the building itself — real flooded structures
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carry sound through walls and floors, not only through the water and air.
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**Corrections.** Kill any statement here with a counter-source and it goes; and if someone can reach a
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primary source for the transmission figure §2 omits, it belongs on this page.