A musical note is being emitted from the stage at the left. Watch it spread across the room in plan view and up the back wall and under the balcony in profile view. The colored bars on the profile view show real SPL drop in decibels at each seat — green is healthy, red is dead. Raise the balcony height to open the soffit angle and watch the dead zone shrink.
The Discipline
The room is half the music
Until 1900, concert halls were built by guess. Vienna's Musikverein, finished in 1870, sounded extraordinary by accident.
Boston's Symphony Hall, planned to copy Vienna, almost didn't get built because nobody could explain on paper why
the Vienna shoebox worked.
That changed when a 27-year-old Harvard physicist named Wallace Clement Sabine was asked to fix the Fogg
Art Museum lecture room, which echoed so badly it was unusable. Working at night with a stopwatch, a portable organ pipe,
and seat cushions from a nearby lecture hall, Sabine measured the time it took a sustained note to decay 60 decibels and
derived the relationship that still bears his name:
T60 = 0.161 × V ÷ A
Reverberation time equals a constant times room volume divided by total absorption. The first equation in architectural
acoustics. Sabine then designed Boston Symphony Hall (1900) on that equation. It opened with the same shoebox geometry as
Vienna and the same long warm reverb — this time on purpose. It is still considered one of the three best concert
halls in the world.
The balcony problem
Sabine's equation is for the room as a whole. It does not tell you what happens to the seats under a deep balcony.
Those seats sit in a sound shadow — the direct sound from the stage reaches them, but the reflections off the ceiling
that would otherwise mix in are blocked by the balcony slab overhead. The deeper the cantilever, the longer the shadow.
Halls with deep balconies have a class of seats that sound flat, dead, and disconnected even when the rest of the room is
perfect. The fix is to keep the balcony depth less than about twice its underside height, or to angle the soffit so the
reflections still reach the seats below. Profile view is where you see this problem; plan view never shows it.
This lab
Two synchronized 2D wave fields run side by side. Same note, same source, same time clock. The plan view shows you what
the room does laterally — standing waves between side walls, the way the back wall returns energy. The profile view
shows you what the balcony does vertically. The lessons live in opposite places, which is why architecture-school acoustics
uses both views and why every existing browser ripple-tank stops at plan.
Why It Matters
Sound is a building material
The point of this lab is not to make you an acoustical engineer. The point is to retrain a habit that pretty much every
civilian and almost every architecture undergraduate has: the habit of treating sound as something that happens
in a space rather than something the space does. The room is not a passive container for the music. The room
is half the music. The other half is the source.
The three states this lab teaches
Too live (absorption < 15%). Wave reflections from the back wall don't dissipate; they pile onto the next
cycle of the note and the cycle after that. The wavefield smears into a continuous blur. In a real hall this is what
a tile bathroom or a marble lobby sounds like — every syllable runs into the next. Beautiful for a cathedral
where the music is the reverb; lethal for spoken word, jazz, anything with rapid articulation.
Sweet spot (absorption ~30–55%). The room returns the note distinct from itself, with one or two
clean cycles of trailing reflection that flatter the original without obscuring it. In Sabine's numbers this puts
T60 somewhere around 1.8–2.2 seconds for a symphony hall, less for opera, less still for a recital
room. It's also the range where the back wall feels present rather than absent. You hear the room
as part of the music, not as a separate effect.
Too dead (absorption > 80%). Everything is gone the moment the source stops. The note doesn't get to
breathe; it just stops. Recording studios are engineered to this state on purpose because the engineer adds the room
back in afterward digitally. As a place to listen to live music it is wretched.
The balcony lesson
Slide the balcony out and watch the profile view. The seats directly under the balcony lose their indirect sound. The
seats just past the front lip of the balcony get a strong sharp reflection off the underside of the slab,
arriving slightly after the direct sound — if the geometry is right this is a useful early reflection; if it's
wrong it's a slap-back echo. The seats on top of the balcony catch the ceiling reflection directly, often
brightly. Three different audience experiences in a band of seats no more than 20 feet apart. Where you sit
in a concert hall changes which room you're sitting in.
Where you'll meet this again
Architecture studios. Auditorium and worship-space sections are designed in profile view
precisely because of the balcony shadow problem.
Live audio engineering. A house engineer chooses speaker placement, delay times, and EQ partly
by reading the room's reverb signature off this same physics, just measured rather than simulated.
Noise control engineering. The same absorption math, inverted — you're trying to suppress
rather than balance the reflections (factory floors, open offices, transit stations).
Civil engineering bridge work. The Ripple Tank lab and this lab share a wave engine. The Concert
Hall lab is the Ripple Tank applied to architectural enclosures; the future Hydrology Flow Flume in ELUSK applies
it to bridge-pier streamlines. Wave math has only one teacher; it lectures in a dozen rooms.
About & Sources
What this is and isn't
Two browser-based 2D wave-equation solvers run side by side at a 200×80 cell grid each, synchronized by a shared
simulation clock and a shared frequency input. The math is finite-difference on utt = c2∇2u
with a CFL number of 0.5, an edge-damping ramp whose strength is driven by the user's absorption slider, and per-cell
walls modeling stage, floor, ceiling, and balcony. The musical note presets are tied to real Hz values; the canvas-grid
wavelength is set by an inverse-frequency mapping anchored to A4 = 440 Hz ↔ λ = 12 cells, so the
visualization stays interesting across two octaves.
What the lab gets right: the shape of how a musical note interacts with a rectangular hall, the way absorption
changes reverb character, the way a deep balcony cantilever creates a shadow zone for the seats beneath it, and the
coupling between plan-view standing waves and profile-view ceiling reflections.
v0.1 — physics-based SPL added
The under-balcony dead-zone overlay (color-coded bars in the profile view) and the SPL readouts are computed from
genuine room-acoustics physics:
Direct sound from a 95 dB source at the stage, attenuated by inverse-square distance loss:
Ldirect = SWL − 20·log10(r) − 11. Blocked if a ray
from source to receiver intersects the balcony soffit (segment-segment geometric intersection test).
First-order ceiling reflection via the image-source method — place a phantom source
above the ceiling at yimg = 2yceiling − ysrc,
compute direct SPL from image to receiver, apply 0.10 ceiling absorption. Blocked if either leg of the path
passes through the balcony.
Reverberant field from Sabine’s diffuse-field equation:
Lrev = SWL + 10·log10(4/R), where the room constant
R = S·α/(1−α), with S the total surface area and α
the user’s absorption-slider value.
Total SPL from incoherent power summation:
Ltotal = 10·log10(10Ldir/10 +
10Lrefl/10 + 10Lrev/10).
T60 reverberation time from Sabine’s 1900 equation:
T60 = 0.161·V/A with V in m³ and A = S·α
in sabins.
So the dB numbers are now meaningful. They’re based on a 100×60×28 ft assumed hall geometry,
omnidirectional source, and frequency-independent absorption — not specific to any one hall, but a defensible
first-order estimate for a generic shoebox auditorium. The color-coded bars in the profile view show the
SPL drop at each seat versus an unobstructed mid-hall reference seat.
Section 4.10.36 · OPA Engineering Suite, sibling to The Horseshoe Vortex (4.10.35). Built at ELUSK Building 10
(College X — Engineering). Triple cross-listed with:
Building 6 · Dolly May Jenkins Center for Music, Theater & Broadcast. The pedagogical
heart of the lab. A concert hall exists to serve the music; this lab teaches that relationship.
Building 10 · ELUSK College of Engineering. The technical home. The wave-equation solver,
cantilever structural cues, and absorption modeling all live here.
Building 13 · The trades-skills shop on the East Quad. The build-it-yourself counterpart.
A real concert hall is a real structure; the steel framing, the soffit angles, the slot diffusers, the wood-stud
absorber panels all come from trades-side fabrication that ELUSK designs and the Bldg-6 musicians evaluate.
Filed under Opathorlokan University, 900 Arkadelphia Road, Birmingham, Alabama 35254. Built by Travis Jenkins
(User Zero) with Claude. The lab exists so that a student can hear, without ever hearing a sound, what a room
does to a note.