Chladni Plate

Project Goal

Design an enclosure for a subwoofer used in the operation of a Chladni plate.

Background

Chladni plates are a way for us to observe the vibrational patterns of different frequencies--letting us “see” sound. Our Chladni plate consists of a metal plate centrally mounted to a speaker in a casing.

When the plate is excited, some areas vibrate and some areas don’t move. More specifically, you are able to see the standing waves along the nodal lines of the plate. The sand moves away from the antinodes, where the amplitude of the standing wave is maximum, and toward the nodal lines, where the amplitude is minimum, forming patterns known as Chladni figures.

When the speaker is turned on, the nodes and antinodes that are set up will form symmetrical patterns over its surface. The positions of these nodes and antinodes can be seen by sprinkling sand upon the plates; the sand will vibrate away from the antinodes and gather at the nodes. Depending on the frequency of the wave, the nodes and antinodes form in different regions. The domain of frequencies that produce patterns is discrete; the radius of the plate must be an integer multiple of the wavelength of the emitted wave in order to create a standing wave interference pattern.
 

Materials

1 x Enclosure Top
1 x Enclosure Bottom
1 x Subwoofer
1 x Amplifier
1 x Flat Plate (Any relatively stiff, lightweight plate works; different shapes create different interference patterns)
1 x Hot Glue Gun
2 x Washer
2 x Nut
1 x Large Bolt
1 x Particulate (Bag of Sand/Sugar/Salt)
1 x Phone or Computer with Internet Access
1 x Drill
1 x Approximately 1”x1” foam square
4-8 x Small Bolt and Washer (for securing speaker to enclosure)
 

Assembly Procedure

1. Place subwoofer on top of enclosure top, and align its screw holes with the screw holes of the enclosure top.
2. Use small bolts and washers to secure the enclosure top to the subwoofer. Hand-tightening is sufficient for this step.
3. Run speaker cables from amplifier into subwoofer through holes in sides of enclosure. Ensure the correct leads are connected.
4. Slot enclosure bottom into enclosure top.
5. Use a generous amount of hot glue to secure the large end of the bolt onto the center of the woofer cone. Ensure that the bolt is properly centered.
6. Drill a hole through the center of the plate. If not using a circular plate, drill through the center of mass. 
7. Screw a nut onto the end of the bolt, above the top of the speaker.
8. Place a washer on top of the nut.
9. Place the foam square on top of the washer, puncturing a hole in the center.
10. Place the plate onto the foam square.
11. Place a washer on top of the plate.
12. Tightly secure a final nut on top of the washer. Wrench-tightening is likely necessary.
13. Congratulations! Your Chladni plate is assembled.

Experimental Procedure

Electronics Setup
Ensure that the speaker cables are connected to the speaker and the amplifier. Ensure that the amplifier is plugged into a wall outlet using the provided cable. Press the “ON” button on the bottom left of the front of the amplifier. Ensure the amplifier is set to the “BT” (Bluetooth) option. Pair your phone or computer to the Bluetooth on the amplifier. The amplifier appears as “BT” on your device. Open https://www.szynalski.com/tone-generator/ on your device. Set the volume slider to 100%.

Chladni Plate Setup
Ensure that the Chladni Plate is level to the ground. And that the nut is tightened holding the plate down. If the plate is not level, place sheets of paper under the base of the apparatus to raise a side until a level surface is achieved. Place a dash of particulate on the plate such that it looks like this, though an exact amount is not needed:

Experiment
Use hearing protection.

Click “PLAY” on the tone generator. Use the SLIDER to sweep the frequency of the tone. Observe the plate to see where patterns emerge, and hover on frequencies that have intriguing patterns. Note: In testing, the frequencies that generate standing waves are inconsistent from trial to trial; however, starting around 440Hz often yields satisfactory results.

It is likely that the plate will not be completely level, and over time, the particulate will drift to one side. In this event, click “STOP” on the tone generator and spread out the particulate. If necessary, place paper under the base of the apparatus to level the plate. Click “PLAY” and resume the lab.

Cleanup
Use a vacuum or broom to sweep up any loose particulate. Unplug the amplifier and coil up the power cable for the amplifier. Leave the rest of the setup as-is. 
 

Design Choices/Discussion

Initially, there was no piece of foam in the system; however, early testing revealed unintended vibrations between the plate and the cone. Ideally, the center of the plate moves exactly in phase with center of the woofer cone; however, hot glue is not a perfect method of securing the bolt to the cone, and the bolt being unsupported in the x and y axis meant that some non-vertical oscillations took place. In order to dampen this vibration, the foam square was added. In addition to this stabilization measure, adding additional bolts could improve the plate's stability.

Possibly the largest challenge during operation is maintaining a level plate, as repeated vibrations combined with a non-level plate result in the particulate steadily moving toward one end of the plate, necessitating frequent readjustments. While using shims to level the apparatus relative to the plate sometimes works, the plate often rotates about the bolt, resulting in an unlevel plate regardless.

Ensure your enclosure has the proper measurements before printing. Mine was for an 8" subwoofer, but yours may be different.