Inactive speakers...some measurements

A while ago we talked about the effect of as few as one inactive speaker in the listening room. It was suggested that I measure the voltage generated by the inactive speaker. OK. I did it. That's the easy part, and the fact that there is a voltage is not surprising. Let's think about what it means.

With steady loud music cranked up to 100 dB (RS meter), the output of an 8 ohm speaker sometimes hit 30 millivolts. If 30 millivolts were applied to this speaker it would amount to 0.0001125 watts.

2.82 volts applied to an 8 ohm speaker is one watt, and produces roughly 88 dB. In general…

0.03 volt……0.0001125 watt
2.82 volts…..1 watt………88dB
5.64 volts....3.97 watts....94 dB
11.28 volts...15.9 watts...100dB
22.5 volts....63 watts.....106 dB
45 volts......250 watts....112 dB

So, if the speaker were driven by the 30 mv (an absolute worst case assumption) its SPL relative to the SPL environment is:

20*LOG(0.0001125/15.9) = -103 dB

This number is referenced to 15.9 watts, not the full power customarily quoted for Hum and Noise. Unlike Hum and Noise the inactive speaker effect (if any) comes down with the SPL, and of course goes to zero when there is silence and when Hum and Noise at –100 dB (referenced to full power) is pretty much inaudible.

I do not believe that anyone's ears can detect a sound source that is 100 dB lower than a prevailing 100 dB SPL. And what would that sound source sound like anyway. Probably much like the 100 dB sound that induced it, making it even harder to detect.

I would still like to participate in a double-blind test for this effect, and I repeat my previous thought that a salesroom full of dozens of speakers may be a different story.

Until that happens…OK you believers…it’s 30 mv at 100dB. How would you analyze it so as to convince me?
Stirring things up again eh Eldartford?

i always enjoy your posts. Keepin it interesting!:)
Eldartford, I agree with you now as I did before.

I'm curious as to what inactive speaker you used, what the room was like and where was the inactive speaker relative to the room and active speakers. What conclusions, if any, does this have on the use of passive radiators?
Okay, I'll bite:

Your measurement seems to make sense on the back-of-an-envelope.

0 dB of sound intensity is, by definition, 10^-12 W/m^2. This is "accepted" as the threshold of human hearing. If you have 100 dB of sound impinging on the face of your speaker that is 10^-2 W/m^2. The area of an 8" diameter speaker is about 0.032 m^2. So the sound power available to excite the speaker is no greater than 10^-2 x 0.032 = 3.2 x 10^-4 W or 320 microwatts.

If you were using an 8" speaker and measured 112.5 microwatts then the sound energy impinging on the speaker driver was converted to electrical energy with about 112/320 = 35% efficiency.

From these numbers it is hard to believe this could ever be a problem even for flea-powered systems.

But then, the human ear never ceases to amaze.

Thank you for making these measurements.
You're missing the point. Not only are the non-driven speakers being excited, they are re-radiating the energy that they absorb out of phase. Depending on the suspension of the drivers and spl's in the room itself, the amount of excitation and re-radiation will vary at a non-linear rate. This is not to mention that some drivers have far looser suspension than others, making them more susceptible to excitation and re-radiation. Using a lower efficiency speaker of the sealed variety as a point of reference, all other speakers will produce greater variances into such a situation.

If you want to do this and do it simply, take a few frequency sweeps in the room at various repeatable volumes and chart the frequency response. Then do the same thing after introducing some good sized speakers that aren't going to be used into the room. These speakers should be relatively efficient and use either a vent or a passive radiator. Duplicate the previous test and then compare the results.

If you really want to do this and do it quickly, borrow some type of device that does digital room correction and run the above tests. It will give you all the variables in a matter of minutes. Sean
sean...It isn't easy to figure out what to make of the data, so what I did was to determine what kind of power level we are talking about. I assumed that this power was all radiated (or absorbed if you like). And my conclusion is that inphase or out of phase it's just too damn small to be heard.

The frequency sweep you suggest sounds like the obvious thing to do if you had equipment, but, in practice I doubt that any instrument would be sensitive enough to even get close to the power level in question. I believe that the ear is much more sensitive than any instrument, but when an effect is large enough for the instrument to detect the instrument gives a description that the sensitive ear cannot provide.

The speaker I used was an aperiodic (damped vented) enclosure containing two LF drivers (8" and 10") which is good to about 30 Hz when powered. It was placed about 2 ft in front of a MG1.6 + subwoofer source. The 100 dB environment was measured right at the inactive speaker.

Regarding passive radiators, I generally do not like speakers that use them, but I can't be sure it is the fault of the PR. Supposedly a PR is functionally similar to a vent but behaves in a more controlled manner and without wind noise. (I don't like vents either). One idea that sounds interesting is to use an actual (inactive) driver instead of a PR, and tune it by L/R/C loading of the voice coil, instead of by the usual way of mass loading the cone. This can be extended to actively driving the "inactive" driver with some sort of signal not the same as the primary signal going to the "active" driver. (In fact I have such an experiment in process).
PR's have the slowest transient response of any vented design that i'm aware of. Just like a port, they also contribute energy outside of their resonant frequency, but do so in different manner.

Rather than having to move air through a tube and having to worry about varying flow velocities, PR's have the added drawback of increased mass. Since the PR isn't moving perfectly in time with the active piston due to this reciprocating mass, and the movement that it has is a direct effect of the active piston having already moved, this is what causes the increase in ringing that one can hear and measure.

In plain English, the PR responds to the active piston AFTER the fact, which is why we have delayed damping and increased ringing. While PR's are great for adding extension, output and bass weight ( perfect for HT ), they lack proper definition and attack / decay characteristics when it comes to music.

Using a passive with a brake on it will probably work better if properly applied, but it is still going to respond to the pressure changes inside the box at any given frequency. In effect, this would be like having a sturdy cabinet that had a small section that was far flimsier in one given area. Tuning that part of the "flexible box" could give you added output when excited, but it is still going to flex ( to a lesser degree ) outside of its' resonant range. When it does this, it will contribute output outside the box according to the pressure changes inside the box.

If you want to start playing games using a PR without killing your transient response, try mounting a passive radiator INSIDE a sealed box on a barrier wall that divides two active drivers. This works best if you use the same approach but with two ( or more ) different drivers with varying sized sealed chambers for each driver.

While each driver / chamber has its' own natural resonance, the other driver / chamber, which is tuned to a different frequency, is now altering the resonance via pulling on the passive. This now changes the volume of each chamber and the associated tuning and pressure inside each chamber. In effect, each driver pulls / pushes the passive according to its' own needs, but, there is always another driver trying to muscle the passive at a different rate. This helps to null any specific peaks or characteristics from any of the individual driver / chamber resonances on their own. Since the individual peaks are minimized and spread out, bass is both more linear and delivered in a more controlled fashion. If everything is done right, you can also gain some extension from this arrangement.

You now have multiple drivers for increased surface area, higher maximum spl's with greater power handling due to sharing the load, minimal peaks at resonance, greater extension, less distortion due to reduced excursion, increased linearity, etc... All of this due to using passive radiators INSIDE the cabinet. The PR does this without contributing any sonic characteristics outside the box.

When you start looking at stuff like this, it is very confusing to say the least. This is especially true when running multiple drivers with multiple chambers and multiple passives. It took me a long time to understand how this works, but believe me, it does work IF you put the time and effort into it. Sean

PS... No, i did not invent this, but i wish i did : )
sean...There probably are enough different ways to configure a speaker system so that every one of us guys on Audiogon (plus Elizabeth) can have their own way to argue is best! Vance Dickason in his "Loudspeaker Design Cookbook" talks about "Augmented PR" where a PR connecting two internal volumes is mechanically coupled to a cone working to the outside. And then there are Bandpass enclosures where all the cones, passive or otherwise, are hidden away inside, and the sound comes out through a hole.

I have always been amazed that PRs behave as they do. With two drivers in a box, and only one powered, it really is difficult to determine by visual means or by ear, which one is powered and which one is passive. In particular the fact that they are in phase (move in and out together) seems counterintuitive. At first thought you would expect the PR to get pushed out when the driver pulls in. That's what happens if you push (at near DC frequency) on one of the drivers. However, at audio frequencies, the pressure variation at the back of the active driver lags driver displacement by 90 degrees and the PR displacement, observed from inside, lags the pressure it receives by 90 degrees. 90 + 90 = 180. But this is 180 degrees on the inside of the enclosure, so the pressure variation outside the enclosure caused by the PR motion is back in phase with the active driver. There is a time delay of one half of the period of the signal. For a steady sine wave signal this would have no effect, but when the signal varies, and is composed of a complex waveform, having many frequencies, all with different half-period delays, the result is a bit mushy.

I have said that vented speakers make excellent bird houses. IMHO, speakers with PR's are little better. However, an idea that interests me is an "active enclosure" where an internal driver, rather than air compression alone, determines the pressure behind the active external driver. The isobaric configuration, where the internal driver sees the same signal as the external one, is the most simple version of the "active enclosure" but the idea can be taken much further. When I get the details figured out, Slappy and I will go into business and become another Bose.
I agree that watching the cones on a woofer / PR system can be pretty interesting. If you have two woofers with a passive ( like Polk 10's, 12's, etc... ), it almost seems like the woofers themselves are out of phase with each other.

As a side note, the active woofer also has to deal with the "back-lash" inside the box from the PR being excited. Obviously, the PR has mass, so it will ring once excited. That ringing translates into vibration that is fed back into the active drivers through the acoustic coupling within the box. With the method that i mentioned, the passive is ALWAYS actively driven by one of the woofers. This is true even if one of the woofers is resonating and has limited excursion since each of the woofers has different tuning / output characteristics. The drive to the PR is always varied as it is being pressure fed by multiple signals of various tunings.

I hear what you're saying about variances in designs, etc... but give this one some thought. It is pretty mind-boggling and quite advanced. This is probably the reason that not too many people mass produce something like this. A lot of math / trial & error involved. Sean
Sean...You are correct that the classical mathematical analysis of loudspeaker designs is ridiculously complex. I prefer to copy designs that I like, and then tweek things a little at a time. Not too appropriate for an engineer like me, but this is a hobby, not my job, where I get lots of practice doing it the other way. I think that a different analytic approach, made possible by development and easy availability of powerful computers would be effective for loudspeakers.

Simulation. The fidelity of simulations has become amazing with the development of generic tools for creating simulations, and the availability of computers with enough memory for the program and the computational speed to run the simulation in minutes rather than days. The performance of the simulated speaker could be output in terms of the same parameters that could be measured on a physical version of the design. For icing on the cake, the program could play music (simulated or prerecorded real) through the simulated speaker system and output an audio signal that the user could listen to on headphones, and, in a matter of a few minutes, hear the effect of design changes that might take a week to try out in the real world. (Of course the headphones would contribute their own signature, but changes would still be recognizable).

Someone, maybe Bose, may have already done this.