Bench Degree·CYMATICSchapter
Appendix A: The Bench
The whole volume’s kit in one place. Every experiment in this book is on this list, so you should never have to stop mid-chapter and wait two days for a delivery. Each chapter names what it needs when it needs it; if you would rather order once and be done, order from here.
One rig carries the book. The plate you build in Chapter 1, a black aluminium disc on a loudspeaker with a small amplifier and a free tone generator, comes back in more than half of the chapters that follow: bowed in Chapter 2, measured against Chladni’s law in Chapter 5, dusted with flour in Chapter 7, rung down for its Q in Chapter 9, metered in Chapter 15, taped in Chapter 20, and turned against the healing-frequency posters in Chapter 24. Build it well once. Most of everything else is in a kitchen drawer.
Nothing here is specified by brand or by part number. Every item is described by function, range or grade, so the list stays orderable from anyone, anywhere, for as long as the book exists. Suppliers change and a printed link dies permanently. A specification does not.
Section 1: The core rig, Chapter 1 and throughout
| Item | Specification | Rough cost |
|---|---|---|
| Aluminium sheet | 1.0 mm (0.040 in) thick, at least 300 × 900 mm (12 × 36 in). Enough for the 300 mm (12 in) disc of Chapter 1, the 250 mm (10 in) disc of Chapter 5 and the 230 mm (9 in) square of Chapter 22. Measure the thickness with a caliper before you buy: every frequency in the book scales with it. | $15 to $25 |
| Matte black spray paint | Satin or matte, never gloss. Two light coats. | $8 |
| Woofer | 165 to 200 mm (6.5 to 8 in), 4 or 8 Ω. Salvaged from an old speaker cabinet is ideal; speakers do get broken on this job. | $0 to $50 |
| Bolt kit | 5 mm (#10) bolt 75 mm (3 in) long, nylon-insert lock nuts, flat washers, two 25 mm (1 in) fender washers, five-minute epoxy. | $8 |
| Audio amplifier | Class-D, 15 to 50 W per channel, with a volume control. A bare board screwed to a scrap of wood, or a cased unit. | $15 to $40 |
| DC power adapter | 24 V, 3 A or more, safety-listed, matched to the amplifier. The mains stays inside it. | $15 |
| Leads | 3.5 mm audio lead from phone or laptop to amplifier; 2 m (6 ft) of speaker wire. | $8 |
| Tone generator | A free browser tone generator or desktop audio editor that sets frequency in steps of 1 Hz or finer, and 0.1 Hz for Chapter 9. | free |
| Multimeter | For the amplifier’s DC check in Chapter 1, the meter check in Chapter 15 and the piezo in Chapter 21. | $15 |
| Table salt | The first-night medium: white, uniform, no dust. | $1 |
| White sand | Washed play sand or fine white craft sand, 0.1 to 0.5 mm (0.004 to 0.020 in). Never crushed, never sieved dry indoors. | $6 |
| Spirit level | Or a phone level app. Sand drifts downhill. | owned |
| Open frame | A box with a large hole cut in it, or two bricks, so the back of the speaker is not sealed. | owned |
Core rig total: about $95 with a salvaged woofer and tools you own; about $140 with a new woofer.
Tools assumed: aviation snips, a file, a drill with a 5 mm (3/16 in) bit, a caliper, a craft knife, a clamp or vice, a hot-glue gun.
Section 2: The phone, and what it replaces
A modern phone is five instruments in this book, all on free apps. Check that each app works before the chapter that needs it.
| App or function | Used for | Chapters |
|---|---|---|
| Sound level meter, A-weighted | Hearing safety at every experiment; the inverse-square law | 1, 15, and throughout |
| Spectrum analyser | Overtones, vowels, your own upper hearing limit | 13, 16, 19, 22 |
| Tuner | Reading a note’s frequency | 10, 13, 19 |
| Slow-motion video, 240 frames per second | Timing a ruler, a wave, a Faraday ripple | 3, 4, 8 |
| Accelerometer | A seismometer on the table; isolation measured | 11, 14, 20 |
| Voice recorder, high quality | Ring-downs and hand claps, read in a free desktop audio editor | 9, 17, 20 |
A second phone or a laptop to run the tone generator while the first one films or measures saves a great deal of juggling.
Section 3: Added for Part I, Chapters 2 to 8
| Item | Specification | Rough cost | Chapter |
|---|---|---|---|
| Violin or cello bow and rosin | A student bow. Chladni’s own instrument, and Chapter 10’s. | $20 to $30 | 2, 10 |
| Square aluminium plate | 200 mm (8 in) square, 2.0 mm (0.080 in) thick, drilled at the centre; a hardwood block 50 × 50 × 150 mm (2 × 2 × 6 in) and a clamp to hold it. | $15 | 2 |
| Steel rulers | Two, 300 mm (12 in) long, 25 mm (1 in) wide, about 0.8 mm (1/32 in) thick. Plus a 150 mm (6 in) rule for Chapter 12. | $10 | 3, 5, 11, 12, 25 |
| Modelling clay | About 50 g (2 oz). | $2 | 3, 11, 25 |
| Small extension spring | 50 to 75 mm (2 to 3 in) long, with coins and a kitchen scale. | $3 | 3 |
| Toy coil spring | Metal or plastic, stretched to 3 m (10 ft). | $5 | 4 |
| Mason’s line | Braided nylon, at least 10 m (33 ft); a screw eye in a block; a full 1 L water bottle for tension. | $5 | 4 |
| Drum shell and black head | 250 mm (10 in) shell with tuning lugs, single-ply black head, drum key. A used shell is fine. A bare head on a hoop will not tension evenly. | $25 to $75 | 6 |
| Hardwood dowel | 6 mm (1/4 in) thick, about 50 mm (2 in) longer than the drum shell is deep, hot-glued to the woofer as a point driver; two more bricks to raise the drum. | $2 | 6 |
| Eidophone | A 150 mm (6 in) PVC pipe coupling 100 mm (4 in) long or a rigid tub; black party balloons; a hose clamp; 600 mm (2 ft) of 25 mm (1 in) hose. | $10 | 6, 22 |
| Plain flour or cornstarch | Fine powder for Chapter 7. Never lycopodium: a cloud of it burns explosively. | $1 | 7, 22 |
| Card, putty, a cardboard box, cling film | Faraday’s card wall and the tent that changes nothing. | owned | 7 |
| Wine glass | Thin, stemmed, plain rim. Charity shops sell them for pennies. | $2 | 8, 9, 19 |
| Rigid plastic lid | 100 to 150 mm (4 to 6 in) across with a rim at least 10 mm (3/8 in) high, for the dish rig; milk, or water with a little ink. | owned | 8, 22 |
Section 4: Added for Part II, Chapters 9 to 14
| Item | Specification | Rough cost | Chapter |
|---|---|---|---|
| Free desktop audio editor | Draws a waveform and lets you read times off it; a play-through setting for Chapter 10’s feedback. | free | 9, 10, 17, 20 |
| Keys, nuts and string | A bunch of keys on a 1 m (3 ft) shoelace; two equal 20 g (0.7 oz) nuts; thread. | owned | 9, 12 |
| Glass bottles | Two or three of different sizes, with a kitchen measuring jug. | owned | 13 |
| Round cake tin | Straight-sided, about 230 mm (9 in) across; ground pepper. | owned | 14 |
Section 5: Added for Part III, Chapters 15 to 21
| Item | Specification | Rough cost | Chapter |
|---|---|---|---|
| Tape measure and phone stand | A tripod, or books. | owned | 15, 18 |
| Moving blankets | Four, about 1.8 × 2.0 m (72 × 80 in), and a way to hang them flat. | $0 to $40 | 17 |
| Clear tube and small speaker | A clear tube about 1.2 m (4 ft) long and 40 to 50 mm (1.5 to 2 in) across; a speaker driver 50 to 75 mm (2 to 3 in) across; a wine cork and coarse sandpaper for the dust. | $10 | 18 |
| Sticky notes | For mapping a room’s loud and quiet spots. | $2 | 18 |
| Black card and compass | Card at least 350 mm (14 in) square, a compass opening to 150 mm (6 in), a white gel pen; a transparency print of your rose-window photograph. | $5 | 19 |
| Soft foam block | Upholstery foam about 50 mm (2 in) thick. | $5 | 20 |
| Foil tape and masking tape | 50 mm (2 in) wide. | $8 | 20 |
| Piezo buzzer discs | Bare, with leads, 27 to 35 mm (1.1 to 1.4 in) across. Buy several. | $3 | 21, 22 |
| Ultrasonic cleaner | Around 40 kHz, about 600 mL; kitchen foil. | $25 to $40 | 21 |
| Ultrasonic levitator kit | 40 kHz, two opposed transducer arrays or one transducer and a reflector, with its own driver board and supply. Polystyrene beads 1 to 3 mm (0.04 to 0.12 in) across. | $15 to $30 | 21 |
| Ping-pong balls and a hair dryer | 40 mm (1.57 in), 2.7 g (0.095 oz) balls; any hair dryer with a cool setting; a cardboard box at least 100 mm (4 in) deep to cover the woofer; a tissue strip on a pencil. | $3 to $6 | 21 |
Section 6: Added for Part IV, Chapters 22 to 27
| Item | Specification | Rough cost | Chapter |
|---|---|---|---|
| Resistor | 10 Ω, 5 W, in series with a piezo disc on the amplifier. | $1 | 22 |
| Hardwood block | About 50 mm (2 in) square and 100 mm (4 in) tall, to mount the Jenny square. | owned | 22 |
| Ring light | Or a circle of white LED strip, for the saucer of water. | $10 | 22 |
| Drink cans, ice, salt | Three steel or aluminium cans; crushed ice; a kitchen scale. | owned | 23 |
| Low-reading thermometer | Reads below -20 °C (-4 °F). A multimeter’s temperature probe often does. | $10 | 23 |
| Macro lens | A clip-on phone macro lens, or a strong magnifier. | $10 | 23 |
| Fifty black lids | Upturned bottle caps or a black ice-cube tray; a 1 mL syringe or dropper; a chilled ceramic tile. | owned | 23 |
| Soft targets | A packet of gelatin dessert made with half the water and set as a 50 mm (2 in) cube in a small square tub; a few grapes; cling film; a deep bowl of water. | $2 | 25 |
| Small flat dish | 50 to 90 mm (2 to 3.5 in) across, with adhesive putty. | owned | 24 |
| Second disc | 280 mm (11 in) across, cut from the same 1.0 mm (0.040 in) aluminium sheet, drilled at the centre; a small coin and tape. | $10 | 26 |
| Pitch tools | A free tuner or tone app that can set A; a free audio editor that changes pitch without changing speed; headphones; a friend and a coin to toss. | free | 26 |
Section 7: The safety gear, which is not optional
| Item | Specification | Rough cost |
|---|---|---|
| Ear protection | Foam plugs and a pair of muffs. Worn whenever the meter reads above 85 dBA. Every chapter that drives the plate loud. | $10 to $25 |
| Safety glasses | Grains leave the plate at speed; glass breaks in Chapters 8, 9 and 19. | $5 |
| Gloves | For cutting and filing aluminium. | $5 |
| A clear screen | A sheet of clear acrylic or a clear storage-box lid, between you and a ringing wine glass. | $10 |
| Damp cloths | Clean up sand and flour wet. Never dry-sweep or blow. | owned |
Whole-volume total, beyond the core rig: about $150 to $300, depending on whether a drum, a bow, a cleaner and moving blankets are already in the house. Most chapters cost nothing at all once the Chapter 1 plate is built.
Bench Degree
Get the degree without the diploma.
Learn the material, not how to pass the exam.