The Chladni Realia Build
~$100 a station · an afternoon to build · nothing dangerous
WP-62 named a falsifiable optics experiment and then priced it out of reach: the DNLS waveguide test needs ~950 kW peak power and a fs-laser-written array, which is a funded-lab collaboration. This paper is the experiment that fits the room we actually have — an adult ESL classroom in Newark — and it tests an exact prediction rather than showing a pretty pattern.
1. The prediction being tested
For a free square plate the classical (Chladni–Ritz) mode functions are combinations of
$f_{nm}(x,y) = \cos(n\pi x)\cos(m\pi y) - \cos(m\pi x)\cos(n\pi y)$
Swap the arguments:
Falsified if: any clean resonance shows sand crossing the diagonal.
This is what makes it an experiment and not a demonstration. Most Chladni setups invite “look at the patterns”; this one says this specific line, every single time — and a student can photograph fifteen modes in an afternoon and check.
2. Bill of materials
Prices verified against Parts Express (Springboro OH) on 2026-08-12; they ship next business day and the exciter showed 3,836 in stock. Items marked est. are estimates I did not verify against a live listing — price them before ordering.
Tier A — the recommended station
| Item | Part / spec | Source | Price |
|---|---|---|---|
| Exciter (2-hole bolt mount) | Dayton EX32EP2-4 · 32 mm · 40 W RMS · 4 Ω | Parts Express 295-231 | $22.98 |
| Amplifier w/ Bluetooth | Dayton KAB-230v4 · 2 × 30 W Class D · aptX HD BT 5.0 | Parts Express 325-503 | $34.98 |
| DC supply for the amp | 19–24 V, ≥ 2 A barrel | any · est. | ~$14 |
| Plate | aluminium 200 × 200 × 1 mm, 5052 or 6061 | metal supplier · est. | ~$15 |
| Centre hardware | M4 bolt, 2 washers, nyloc nut | hardware store · est. | ~$2 |
| Speaker wire | 16 AWG, ~1 m needed | Parts Express 100-034 (100 ft spool) | $12.98 |
| Spade terminals | 0.110″ female, 50 pcs | Parts Express 095-286 | $5.98 |
| Medium | fine dry sand, or lycopodium powder 50 g | craft/lab · est. | $0–12 |
| Signal source | tone-generator app on the student's phone | — | $0 |
| Per station (wire & terminals amortised) | ≈ $95–105 | ||
Tier B — class set economy
Swap the KAB-230v4 for a generic TPA3116 Class-D board (~$12 est.) and drive it from a 3.5 mm cable instead of Bluetooth. Saves about $23 a station; costs you the phone-pairing moment, which is pedagogically the best part. For six stations:
| Tier A ×6 | Tier B ×6 | |
|---|---|---|
| exciters | $137.88 | $137.88 |
| amps | $209.88 | ~$72 |
| supplies, plates, hardware, medium | ~$260 | ~$260 |
| wire + terminals (one spool, one pack) | $18.96 | $18.96 |
| total | ≈ $627 | ≈ $489 |
3. Assembly
- Drill one 4.5 mm hole at the exact centre of the plate. Centre accuracy matters more than anything else in this build — measure both diagonals, mark the intersection.
- Bolt the exciter to the plate centre: bolt → washer → plate → washer → exciter mount → nyloc. Snug, not crushed; the plate must ring, not thud.
- Mount the exciter body to a heavy base (a bench vice, or a block of wood clamped down). The plate should be horizontal and free at all four edges.
- Crimp spades, wire exciter to amp output, connect the DC supply.
- Pair the phone over Bluetooth. Open any tone-generator app.
- Dust the plate lightly with sand. Sweep slowly from 100 Hz upward.
Build time is an afternoon for the first one and about twenty minutes each after that. The only tool that isn't in a kitchen drawer is a drill.
4. As realia — what it does in the language classroom
The object earns its place because it forces the vocabulary rather than illustrating it. A student at B1 can see a node before they can define one, and the definition then has somewhere to attach.
| CEFR | Task on the object | Operator |
|---|---|---|
| A2 | Label what you see: sand, line, loud, still, edge, centre. One or two sentences. | C |
| B1 | Compare two frequencies. “At 420 Hz there are four lines, but at 680 Hz there are eight.” | C → K |
| B2 | Justify: why does the sand move away from where the energy is? Write a paragraph. | full G |
| C1 | Critique the test: what would make the diagonal fail? Name the confound. | G + normal form |
| C2/D1 | Photograph 15 modes, tabulate, and write the 150-word result — including a negative one. | U |
The C1 task is the real one, and it has a correct answer: asymmetric clamping. The diagonal is nodal because the whole system is symmetric under $x \leftrightarrow y$. An off-centre bolt, a plate that isn't square, or a clamp that grips harder on one axis breaks that symmetry and the prediction with it. A student who finds that has done the physics.
5. Protocol & what to record
- Sweep slowly. Resonances are narrow; move in ~2 Hz steps near a figure.
- At each stable figure record: frequency, photograph from directly overhead, and a yes/no on “is the diagonal clear of sand?”
- Do both diagonals. A square plate is symmetric under $x \leftrightarrow y$ and $x \leftrightarrow -y$; both should be nodal.
- Then break it deliberately: loosen and re-bolt 10 mm off centre, repeat. The diagonal should degrade. This is the control, and it is the part most demonstrations skip.
- Report the count: modes observed, modes with a clear diagonal, modes without. If any mode fails with symmetric mounting, that is a result and it goes in the write-up.
6. Where this connects
| cymatics.html | the browser Chladni simulator — students can predict a figure on the phone, then produce it on the plate |
| ICHEP pointers | EXP13 · Cimática com Máquinas, CETECH foyer, UFRN — the exhibit this turns into an experiment |
| WP-62 §3 | the DNLS experiment this replaces at classroom scale, and why that one needs a lab |
| Hour House · AULA | the lesson programme this is realia for |
This page is the sourcing and protocol sheet. The student-facing version — how to ask for instrument time, what New Jersey's $40,000 R&D voucher actually is and who may apply for it, and the lab-partner pre-registration form — is Get a Bench · Build a Device.