After all the design work and all the construction was complete, I still had to listen to music. Of course, for a long time, I thought these were the best sounding speakers ever to land on this planet. After a while, however, I began to notice some things that weren't perfect. I made a lot of adjustments to the crossovers, moved the speakers around in my listening room and listened some more. The mid bass was always a problem for me. There was something there that didn't belong. The early prototypes on the flat baffle and the final version with the curved edges, all had a little extra presence when an upright bass was played. Finally I thought to run an impedance sweep on the bass/midrange Dynaudio 24W75s. These drivers cover the frequency range from 50 to 800 Hz. Sure enough, resonances showed up at 43 Hz and at 62 Hz. When I ran this same impedance data with the speaker laying down or with just the raw drivers, it didn't show up. With the speaker in its final resting place on the floor of my living room a couple of interesting things showed up. The moving mass of these 9 inch drivers is only 18 grams each for a total of 36 grams. The complete speaker ways 65 pounds. That is a ratio of 1 to 820. If you have something like a 15" Lambda dipole woofer at 90 grams each, the equivalent ratio would require a baffle weight of 162 pounds for each driver or 650 pounds for a baffle containing four drivers. Whew!
I have recreated the process I went through to eliminate these resonances below. Everyone thinking about building a dipole speaker should pay attention. It was a real eye opener for me!
Initially I set the speaker up to rest on three spikes. The base of the speaker is bolted to a piece of 1 1/2 inch diameter aluminum bar that is 13 inches long. The spikes are made from 1/4-20 bolts with the heads cut off and rounded on a grinder. The cross section through the baffle is shown below.
The Impedance sweep of this configuration was a little problematic. As you can see below, there was a resonance at 43 Hz and at 62 Hz. This may be what I was hearing during my listening tests

I tried some Acoustistuff stuffing behind the drivers first to see if that had any effect. As you can see, it had a very slight effect.

Next I tried some added mass. I put 5 pounds of modeling clay inside the half-round edge of the baffle. It was centered right between the two bass drivers. This really helped with the resonance at 43 Hz, reducing it considerably. The resonance at 62 Hz was not affected at all.

Adding 5 more pounds of clay helped a little more, but still did nothing about the resonance at 62 Hz.

Next I tried some soft feet rather than the spikes. Now we see some real improvement! I used Gel mouse wrist pads. With just two of them I was really happy.

Using three Gel pads was even better. This looked good on paper and sounded good also. Now Ray Brown sounded like he was playing bass at the other end of my living room, where before he was sitting in my lap. BIG improvement.
The only problem with this arrangement was that the speakers were very "tippy" and I was afraid they would fall over if someone brushed up against them.

I built another "foot" and put spikes on each end to match the foot I already had. I figured this would help keep the speaker from falling over if someone bumped into it.

On four spikes, the impedance sweep again showed major resonances at about 65 Hz.

Changing the four hard spikes for four soft Gel pads reduced the resonances to reasonable levels. There is still a few small ripples at 70 Hz and 125 Hz.

This configuration went back to three pads but left the two long feet.

Again with three pads, but with the single pad turned 90 degrees.

I went back to the original configuration with three feet on soft pads and repeated the data from that setup exactly. This is clearly the superior arrangement.

Now I tried the three feet configuration with no stuffing. This looks even better than with the stuffing.

I put the rear grill on to see if that would have any adverse effects. It doesn't seem to.

Next I checked the right speaker in basically the same configuration to make sure it was telling me the same thing. There is no added mass in this speaker. It looks exactly the same.

Here is a closeup picture of the final pad configuration. This sounds the best so I guess I will learn to live with the possibility that they may get knocked over. The speaker is sitting on a piece of Corian that is stuck to the floor with 4 glops of duct sealant. My floor is very uneven and without the leveling capability of the spikes I have to have an artificial flat spot to set the speaker on.

This last picture show the complete speaker with the rear grill installed.

I learned a lot by doing these tests. Unless you do vibration analysis for a living, I highly encourage you to do a lot of experimenting. There is no easy way to guess what kind of vibration modes your particular design may have. On this design there are a number of vibrating masses. The cone, the driver frame which is soft mounted to the baffle, the baffle, the leg at the bottom of the baffle and the floor itself can all be vibrating together or in opposition to each other. I would guess that if the leg on the bottom of my speakers was braced up to the mid point of the baffle that it would present entirely different vibration modes.
If I get a chance to get a stick-on accelerometer I will certainly try that. All I have done here is reduce certain vibrations that occur in the driver itself and show up in it's impedance. The baffles are still vibrating a little and I don't know how much this influences the sound I hear. The amount of vibration is about what you would feel with a normal box speaker. I know they sound better now than they did on the spikes. In fact they sound great! I think I'll take a break from all this HTML and go listen to them. Yeaaah.
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