MJK or somebody: need some math help

[Chaz H]

Just for fun, I'm trying to determine how the Eminence Deltalite-II would perform in a U- or H-frame. I wanted to get an idea of the ultimate system Q for the driver in a U-frame, so I tried using the equations that MJK has given in his article. I started with the equation for Qed:

Qed = (Mms + Mair)*Fd*Re*Bl^-2

When applied to the eminence alpha 15, MJK gets a result of 1.792. However when I plug the deltalite's info in...

(72+22)*36[est.]*5.29*15.7^-2

I get a result of ~72.62. What am I doing wrong to get such a dramatically different result?

 

[Chaz H]

Same thing happens when trying to solve for Qmd. According to the same paper I solved Rmd as 4.189, then when I applied that to the equation for Qmd I got 807.83. The equation given for Qmd is:

Qmd = (Mmd +Mair)*Fd*Rmd^-1

or

Qmd = 94*36*4.189^-1

however, if I change 94 to .94 I get a more reasonable solution of 8.07. Is that my error?

 

[Chaz H]

Well, I might have solved the problem. I was off by a factor of what, 100? By changing a gram from 1 to 0.01 in the equation I get more reasonable results.

U-frame:

.94*36*4.189^-1 = 8.07 Qms

.94*36*5.29*15.7^-2 = 0.72 Qes

(1/0.72+1/8.07)^-1 = 0.661 Qms

predicted rolloff = 55Hz


H-frame

1.14*36*4.189^-1 = 9.79

1.14*36*5.29*15.7^-2 = 0.88

(1/0.88+1/9.79)^-1 = 0.807

Fd = 32

rolloff = 40hz



That sounds about right to me, although of course I am fudging the numbers a bit with regard to Fs. Without measuring I can't be entirely certain what a mass of 22g (or 44) will have on a cone of 72g weight compared to the alpha 15, which has a cone weighing 59.8g. If SPL is consistent with the A15 in these configurations, then the deltalite should still be around 89-90db efficient.

But I have another question now, which MJK or some other guru can answer if he or she likes. Will a U-frame of double the depth (in this case, 15" as opposed to 7.5") have the same massing effect on a speaker cone as a similarly-sized H-frame, or is the effect diminished?

 

[Jim Shearer]

Somebody else should check this, but IIRC, making the U frame deeper than 7.5" will result in resonance down in a region where you don't want it.

Cheers, Jim

 

[Chaz H]

That's what I recall too, but I wasn't sure if there was some leeway.

 

[GM]

Not really, unless you flare the sides out to at least a 12 deg included angle to turn it into a 1/2 WL resonator with good 'slap' echo decay same as a LEDE room design. When straight back it's a 1/4 WL resonator, so even before factoring in a large end correction that will further lower it, 7.5" is already down to ~13560/4/7.5 = ~452 Hz and you want it to be well above the XO point.

GM