By Pat Brown
In this article, Pat Brown discusses the uses of a dodecahedron loudspeaker and how to build one.
A polyhedron is a multi-sided three dimensional shape. A dodecahedron is a 12-sided polyhedron, each side being a pentagon. A dodecahedron loudspeaker, or dodec, for short, has a full-range loudspeaker mounted in each of the 12 sides.
So what is this thing for? Well first, it would make the worst possible loudspeaker for speech reinforcement, since its energy is radiated in every direction from the device. I prefer to call it a “random directivity” loudspeaker rather than “omni-directional” or “spherical” since omni implies that the energy is radiated equally in every direction at every frequency. The dodec does approach omnidirectivity at lower frequencies where the longer wavelengths allow better coupling between the 12 loudspeakers. Dodecs are useful for acoustic testing, when the goal is to excite the room as much as possible for the purpose of measuring the decay times of the space. This makes a good starting point for an array design, as it allows the critical distance of the room to be considered apart from device directivity. Acoustic theory (and common sense) tells us that critical distance, along with the maximum speech communication distance, will increase as devices with higher directivity are employed.
In addition, a dodec makes a great conversation piece. Where do I get one? There are some excellent models that are commercially available. For the more adventurous, they are not too difficult to fabricate if the right tools are available. In fact, only one shape is involved – a pentagon. The major decision is the size of loudspeaker to use. I chose a 4-inch unit, which allowed my dodec to be kept small for traveling purposes. The loudspeaker should provide usable response from 100 Hz to about 10 kHz, no great feat for a 4-inch transducer and some equalization. The acoustic comb filtering from the overlap will make a smooth frequency response impossible. The goal here is to excite the room, not to sound good.
Building a Dodec
- 1. Start by cutting a 7.5 inch length off of a 4’ x 8’ sheet of birch plywood. A table saw or panel saw works well for this purpose.
- 2. Use a table saw to slice the board into 7.5 inch squares. Twelve will be required.
- 3. This step is critical. A compound miter saw is suggested. If you don’t own one, they can be rented at the local rental house, since carpenters require them for installing crown molding. Set the saw for an 18 degree angle (900 – 720) and proceed to cut the squares into pentagons. I simply marked the saw guide at 4.5 inches with a pencil and rotated the square after cutting each face.
- 4. To cut the correct bevel on the pentagon sides, set the vertical angle of the saw at 33 degrees ((1800 – 1140)/2), keeping the horizontal angle at the original 18 degrees. Recut each side using this setting. While it would be possible to make both cuts at once on the squares, I found it easier to control the saw by breaking it down into two steps.
- 5. The pentagons are now ready to assemble. Clamp one down to a firm work surface and see if the others fit together correctly. They should if you have done everything correctly up till this point. I used a 1.25 inch brad nailer (air powered) to assemble the sides. Apply wood glue liberally to both surfaces prior to nailing. Internal braces should not be necessary, since the very nature of the shape makes it nearly impossible to com- press the dodec or pull it apart.
- 6. Use a 4-inch hole saw to cut the loudspeaker holes. I went a step further and recessed the loudspeakers using a router. If you are going to do this, I recommend finding some round loudspeakers. The stamped-frame units that I used were more rectangular in shape, which required me to make a router template.
- 7. The loudspeakers must be wired in a series-parallel configuration to get a total impedance close to 8 ohms. See the wiring diagram (Fig. 1). The actual impedance was about 6 ohms, which should work with virtually any power amplifier.
After completion of the dodec, I performed some MLS measurements in my office. The measurements (next page) show the log-squared response of the full decay of the office. Note the density of the energy tail as it trails off into the noise floor. Also shown is the first 100 ms of decay. Again, note the large number of early reflections that result from “bombarding” a room with energy. The next test replaced the dodec with a 4” bookshelf loudspeaker. The level was adjusted to provide about the same direct sound level as the dodec. Compare the “room” response of the bookshelf loudspeaker with that of the dodec and note the difference in the energy density of the decay.
Dodecs are useful for a variety of acoustic tests. When measuring reverberation times (RT60) of rooms, the dodec is used to excite the room as much as possible, since directional sources may not “tickle” the room enough to get good data. Remember that the RT60 is a room parameter. Using a dodec does not change the RT60 of the space, but drives up the level of the reverberant field so that it can be measured. This is quite the opposite goal of a good sound system, whose purpose is to provide an adequate direct sound field and as little room excitation as possible. The dodec is also useful for studying the stage layouts in performing arts spaces. The early-reflected field is vital for reproduction of instrumental music. Placing a dodec at the location of low-directivity instruments allows the behavior of diffusors, reflectors, etc. to be evaluated.
In conclusion, if you are measuring room parameters, a dodec is a useful tool. Place it in the space, excite the room and study the reverberation and reflections that result. When designing a sound reinforcement system for the space, try to accomplish exactly the opposite. The measurements show that directivity is a valuable tool for providing an adequate direct field without exciting the room. pb