f3 of passive radiator-system

[Svante]

The free version of Basta! gives these curves, which are not too different from RonE's curves. They are not perfectly equal, but then again there is some guesswork involved in my parameters fed to the program.

[MCPete]

My system has two woofers total, with one of them functioning as a passive radiator.

Ron E.'s simulated f3 = 58 Hz corresponding to Vb = 18L is closer to my measured f3 = 68 Hz. According to Table 3.1 in the Loudspeaker Design Cookbook, for Qts = 0.45, I should have been able to get f3 = 48 Hz.

As I understand Ron E. , woofers are not very suitable functioning as a P.R. due to lacking relatively more mass to begin with, are not high compliance and have low Q. If I do use a woofer as a P.R., I'm wondering if Qms is equal to Qmp, and what value of Q of the passive radiator would result in the best performance?

By the way, in post #9 I incorrectly state that in Weems' chart relating alpha to Qts for vented systems, alpha = 1.5 corresponding to Qts = 0.45. Actually his chart is a graph of Vb/Vas as a function of Qts, so alpha correctly equals 0.67.

Many thanks to Ron E. and Svante for their simulations of this P.R. system.

-Pete

[Svante]

Originally posted by MCPete
My system has two woofers total, with one of them functioning as a passive radiator.

Ron E.'s simulated f3 = 58 Hz corresponding to Vb = 18L is closer to my measured f3 = 68 Hz. According to Table 3.1 in the Loudspeaker Design Cookbook, for Qts = 0.45, I should have been able to get f3 = 48 Hz.

As I understand Ron E. , woofers are not very suitable functioning as a P.R. due to lacking relatively more mass to begin with, are not high compliance and have low Q. If I do use a woofer as a P.R., I'm wondering if Qms is equal to Qmp, and what value of Q of the passive radiator would result in the best performance?

By the way, in post #9 I incorrectly state that in Weems' chart relating alpha to Qts for vented systems, alpha = 1.5 corresponding to Qts = 0.45. Actually his chart is a graph of Vb/Vas as a function of Qts, so alpha correctly equals 0.67.

Many thanks to Ron E. and Svante for their simulations of this P.R. system.

-Pete

...my tip on this is to throw out those old formulas and start simulating instead. The formulas were great at the time when there were no computers around and they represent, imo, an oversimplification of a more complex reality. You get much closer to that reality with simulations and measurements.

Regarding the best Q for a PR: It should be as high as possible. Just as there should be as little flow resistance in a vent, there should be as little mechanical resistance in a PR. That means that the Q should be as high as possible.

I think the biggest problem in this design is that there always is a dip in the response near the PR free air resonance. For dedicated PRs, this resonance is typically well below the useful frequency range, but for this woofer it is 45 Hz and theis limits the frequency range.