Alright, to this point we’ve addressed the design of the optimal box volume for the ported speaker without ever having talked about the length and diameter of the port. but let’s move this mouse off. But both, but both of them can be computed and I’m basically giving you the equations here. so this this basically defines the minimum diameter of the port, and that's related to the resonant frequency associated with the box and volume, basically of the the volume associated with the maximum displacement possible for a given transducer. So you know, the throw of your speaker is associated with the x max, is the maximum displacement that your transducer itself has. And so, V sub d is related to x max in the area associated with the driver. so you can see that d is the actual diameter of the transducer itself, so applying this relationship you can easily calculate the minimum diameter, diameter the port, and that's so that you don't you know, it's to prevent excessive port noise If, if you make the diameter too, too small, you can get a wheezing sound, if you will, in the port. So, this, this helps you avoid that particular issue. So the length, then can be computed from the equation as shown here. And I, basically I'm using, still using metric units. but it's related to the the chosen diameter of the port, so D sub v is the chosen diameter of the port. It's gotta be bigger than B sum m, so D sub v is greater than D min. And you see we still have the resident frequency associated with the box and the volume of the box and this will give you the length, and there's a great reference for the equations can be found at this website, actually. if give me just a second and I will pull that up on the screen and we'll take a look at that. So, if you follow this, this is a, this is a set of equations, speaker equations that Bill McFadden placed up here and you know originally in 1993, I guess last modified February of '07. but basically very nicely done, he defines all the variables associated with the peel small parameters you know, again, the minimum diameter diameter the, of the port, the vent itself. Tuning frequency, and then basically will take through all of the design. I guess I should slow down here, I forget that dawn, on this screen-capture mode, you get a little bit pixelated I think when I scroll too much or too fast. Let's roll down to the bottom here. these goes through the closed box design. here's some great, great pointers and details. Talks a little bit about sound pressure level and then gets to the design equations and you can see, you know he's constants, he's got the speed of sound at 345 meters per second, he's got pi to a few significant figures density of air and then there's the closed box design. we've dealt with that already earlier. And here's the ported design. And you will see the frequency dependent equations. If you remember that's what I used ear, a little bit later to calculate the the frequency response that I plotted so that we could predict what the frequency response was. You can do the same thing for the close box design if you want to estimate the frequency response for the close box design. And as you recall, and you know, we've already been, again, back to the design tool. But this is you know those, those parameters can allow you to estimate the frequency response here for the sealed or closed box design and imported design. We didn't discuss the band pass design.