Help understanding the physics of Vas

[sdad]

Vas, as I understand it is the equivalent volume of standardised air that represents the compliance (Cms?) of the speaker in question. I have been told that Vas = Vb((Fb / Fs)² - 1). From this formula I notice right off that for Vas to be positive Fb must be greater than Fs. Since there are no illegal states, Vas can be virtually any real value.

Issue here is Fb. Fs is resonance in open space, Fb is resonance in a closed environment, where the speaker is working against an increased load created by a volume of enclosed air. Because of the additional stiffness created by the enclosed air I visualize the resonant frequency of the speaker to increase, and from data I've seen, that is what happens. But is this necessarily so?
I have speaker in my possession which does quite the opposite, at least as I am measuring. I can place the speaker flat against my floor and measure a markedly reduced resonant frequency. ??????? Same results into 28 liter box.
Now, I am using small signals, output voltage from amplifier is 1 volt. I have checked amp out volts both free air and closed box at both frequencies. The series resistor for watch for current is non-inductive (even if inductive, that would be wrong way). I have noticed that Fb is actual, but have not measured Q in box. There is no dual peak as you might see in a tuned box

I am curious as to what I am doing wrong, or if all is ok with the test setup, what is the physics at play here? I already have boxes under way for this set of speakers, and will use active filters to compensate, if needed, but why the negative Vas???

[AndrewT]

Hi,
the T/S parameters are the result of small signal testing, but also in free air with no interfering reflections nor sounds coming to the cone. The cone and Voice Coil act as a microphone and do generate voltages which will seriously affect the measurement results you are trying to take.

Fs is the resonant frequency in free air with no reflections. I have seen it stated that the driver frame must be vertical, i.e. cone pointing horizontally and supported by two completely different methods.
Tightly bolted to an immovable very stiff frame or hanging from a thread from a sky hook, a mighty strong thread for an 18inch driver and I can confirm that the light pendant in the middle of the room did not break loose. I have never compared the solid frame support to the hang by a thread result.

The Fb test must be done in free air. Again no reflections nor wind noise to affect your measured results.
I use the added weight Vas method to avoid having lots of dummy boxes.

Fb takes account of both mass and the compliance of the free air driver and adds on the compliance of the air sealed into the box. This combined compliance must be stiffer than the free air compliance. It cannot be any other way.
This leads to Fb>Fs always.

[sdad]

AndrewT...Thanks for taking the time to respond back to me. What you have done is reiterated my concern! How did this happen????? Most likely it has to do with my test jig. I have no problem with that. What I want to do is fix my ways, so I can take meaningful measurements.

What I have done is cookbook, followed procedure outlined, among other places, in ESP website. The free air was done with the speaker facing upwards, resting on the magnet .
I will try suspending in a different fashion. I suspect that it is the free air measurement that is at fault here ( Reflections from the surface that the speaker is resting on), rather than the on the test box.

I'll try it and see.

Thanks again.

[wintermute]

I think Resting the speaker on it's magnet is your problem, yes you will get reflections off the floor, but probably more importantly you are working against gravity resting on the floor will have even more of an effect if the speaker has a vent in the magnet I suspect...

I've tried both hanging and clamping and preferred clamping. I got more consistent results and smoother impedance curves when clamping, I think the problem with hanging was that the speaker could still move with respect to the air around it (which would be less of a problem the heavier the driver was, I did the comparison with 5" drivers).

Tony.

[speaker dave]

Andrew is correct that box mounting will always increase total stiffness and always raise resonance. Be aware that laying on the floor will give some extra mass loading. Also make sure that laying it on a surface doesn't close up any rear vents that might change apparent stifness. Suspending by hanging can allow the chassis to move and will perturb the resonance also. Rigidly fastened away from surfaces is the goal. Mounted on an open baffle can be good.

You can also use the added mass technique to calculate effective mass then calculate Cms or Vas from that.

Be forewarned that high accuarcy in T/S numbers is usually elusive.

David S.

(Edit) I see that Tony was a faster typer than me!

[sdad]

Regarding the added mass technique. This would be a relative value change, would it not? In other words, if I were to place the speaker in the same position for each measurement, before and after the addition of the mass, then what I am observing is the difference in the 2 values with same environment, not basing my calculations on 2 absolute values from 2 different locations. Understanding the need for accuracy in weighing the mass, this approach might actually improve my accuracy. Certainly worth a try. Don't see how I can do worse than getting a decrease in resonance just because my outdoor temp is also in the negative and I'm too whimpy to put on a coat.

As a side bar, I appreciate how folks are jumping in here. Europe, Australia, Canada. Wow!!!!!!

[AndrewT]

minus outside ! Is that C or F or K?
The surround and to some extent the spider will change compliance as the temperature changes.
Very low temperatures will result in very low Vas measurements.
A new surround also results in a low Vas measurement.

The driver needs to be run in at normal operating temperature and tested at the same operating temperature.

[sdad]

Actually, Andrew, I was referring to myself, forget the speaker!. Yikes, degree K?... Deg F, and a slight exaggeration. Single digit though. I am somewhat intrigued by the idea of the mass measurement approach. If I can eliminate variables in gathering of data, then I am all for that approach. Kinda like minimizing even order impacts.

[AndrewT]

The added mass method is approximate and the higher the proportion of the added mass the worse the error becomes.

If your mms is 50gm then don't add 25gms, 50% is far too high.
5gm (10%) should give a reasonable result.

Something you can do is add 5, 10, 15, 20, 25gm and plot the graph of Vas vs added mass. You will see the slope of the line and that the slope gets worse as the mass increases.You can guess at what to expect with 1gm and then do a check measurement to see if you can read at the resolution to detect the frequency change.
I use a lead sheet shim stuck on with double sided sticky tape. easy to hammer out to 5mil, 5thou, ~0.1mm thick, stick on the double sided tape and rub it on well. Cut with scissors to the weights you require. You might have to go back to your school and ask the science teacher to let you weigh your samples. Remember to remove the backing paper before weighing.

[wintermute]

Excelent idea with the hammered lead Andrew! I always struggled with the added mass, I can't actually remember whether I used large washers sticky taped on the dust cap or rolled up blue tac around the dust cap the last time, both were a bit hit and miss if I recall correctly... I bought myself a little scale accurate to 0.1g twas rather expensive though, probably more than the drivers!

Tony.