Most spec sheets come with the dimensions and the bolt hole parameters. We saw that earlier in the sketches I provided. And you should use this in planning your design and also the mounting configuration. You always want to mount the transducers from sorry about that, mount all the transducers from the outside of the enclosure. if you mount them from the inside you end up with some diffraction and you know, round the opening of the box itself. And you know, some added dynamics that, that are not desirable. So you always mount the the transducers from the outside of the box. So, you know, they'll have a, a flange on them if you, if you imagine the cutaway of the box looking something like that. the speakers will have a flange and the flange will sit on the outside. And then of course, they'll fit inside the whatever opening you that cut in the box. But mount, mount them on the outside of the box here, so this is the interior of the box, all right? So with that those basic guidelines those should apply whether you're designing ported enclosures or you're designing an enclosed box. But we're going to start today talking a little bit more about closed box design. And so for the moment we're going to go back to our old discussion of the Helmholtz resonator. And if you recall when we put a speaker in a box, the enclosed air in the box actually adds stiffness. So if we have a speaker with a diaphragm of a given mass and it'll have its own spider and suspension system. So this is the tranducer, these two components are fot the transducer on its own. But once you set that transducer in a box, you ger an added stiffness that's associated with the enclosure and I've kind of sketch that over here. you know, where we've, I, I show the box and the transducer itself, and of course there's a, a stiffness associated with the speaker. The, the spring doesn't sit up here on top of the transducer, I just sketched it symbolically. And then we have some stiffness associated with the enclosure, the box itself. but it turns out that the the total stiffness of the box. Or I mean the total stiffness for the design is going to be the sum of the stiffness of the speaker itself plus that of the box. And so, if you can calculate a new, natural resonance frequency associated with the box or you know, the speaker designed in the box. Based upon the mass of the vibrating diaphragm of the speaker and then of course the total stiffness in the box. Now, box stiffness we already covered earlier, but I'll, remind you again with the equation here that the box stiffness depends upon, you know, some basic parameters. Such as the density of the air, the speed of sound in air, the volume of the box and then, of course, the radius of the driver. so you should remember, for a given box size/volume, the stiffness really depends upon the area of the transducer, or the radius of the piston. So a fixed box size doesn't have a fixed stiffness. A fixed box size has a stiffness that's dependent upon The radius of the speaker, okay? And so if you end up with a smaller radius, then you're going to end up with a higher stiffness. If you end up with I mean, a smaller stiffness, if you end up with a larger radius, you're going to end up with a a larger stiffness. So they're proportional but, you know, it's proportional in terms of the square of the radius and then the square of the area. it's an important part of the design consideration. Some basic Thiele-Small parameters required for design basically are the speaker or transducer, free-air resonance. This is with no box and then Qt, Q sub ts. the ts is a subscript just known to represent the total Q of the driver at resonance. And again, the Q can be thought of an amplification factor at resonance. The greater the Q, the sharper the resonant peak. So I, I shown this here in a diagram that I generated for increasing Q. And you can see that, you know, basically our our resonant peak is in this domain here. And as Q increases, and that's what this arrow is here. The, the peak gets taller, so the response becomes sharper, if you will, around that frequency. And you know, we can debate over which curve might be an optimal curve if we were looking at the response of of of a speaker itself. The other thing that we need in the design from the Thiele-Small parameters is the speaker's compliance. the speaker's compliance is the reciprocal of the stiffness. But the way they're, it's specified in the Thiele-Small parameters is the equivalent volume of an enclosed box that would yield a certain stiffness. So, it's, that's a simple expression basically it, it, it's just a different way of expressing the spring constant. Because we can ca, calculate based upon the, the previous equation which relates to stiffness of a box to a volume in an area. we can basically assume that we have a box that has this stiffness identical to to that of the speaker. And then we can solve for that volume. And that's, that's the volume that specified with the Thiele-Small parameters. you should also note that when I talk about compliance, compliance is just the reciprocal. This is the compliance, that's the reciprocal of the speaker's stiffness, alright? [COUGH]. So if we're given um, [COUGH], the three previous parameters. For any given box volume, you can calculate the following. you can calculate the closed box resonance, that defines the low frequency bandwidth of the speaker. you can co, compute the speakers reg, resonant magnification for a closed box design. And you can also, this should be magnification, sorry, not magnificent, but magnification. And then you can compute the 3 dB frequency. At which the bass response is, reduced by 3 db and that's called the cutoff frequency. mainly because that's where you start to get diminishing response of the bass. you're on the downward slope, in so to speak in terms of the bass response, alright? most closed box designs will aim for a target of a queue for the closed box to be somewhere between you know 0.7 and 1.1. if queues, if the Q of the closed box is less than 0.7 the low end response really deteriorates. Remember the the curve that we looked at earlier where we were looking at the you know, the peak responses like this. And you know, as, as it gets smaller you, you're, you end up this was increasing Q if you remember. And the smaller domain you get this roll off at low frequencies, so you know, you can see you know. If I were just looking at this frequency and maybe the response you know, being normalized here. You got a lot more response here than you do here and you're really way off on the low side. So, that's for, for small queues. When the Q of the closed box is much greater than 1.1 then you end up with this peaky response or the you know, has this real boomy sound to it. And again that's because, you know the higher queue is going to give you this, this kind of peak here. And what we're really, what we really like to have you know is, we really like to have this really flat perfect frequency response that was cut off really sharply. And, and gave you a very consistent and flat frequency response over the audible range. Designs end up being compromises and, you know, sometimes the curve looks more like that and sometimes it's more like this. And that's part of the overlaid ensign process, but let's, let's work an example here. Let's assume we're given a driver, okay, with a a free air resonance of 30 hertz. And a total queue of 0.5, and a volume, an equivalent volume for the stiffness that's 283 liters. And let's choose a Q for the closed box of one, so we'll choose a simple number [LAUGH] in the range that we were we were given. And here are your design equations for computing the design of your box. you first want to get the ratio of, of your desired Q, Q of the clothes box, to that of the total Q for the speaker. for our choice that, that ends up being 2. we want to be able to compute the volume of the box. The ratio of the volume of the box to that of the volume of the equivalent box of the, relating to the speakers compliance, VAS, is related to the square of the Q of the closed box to the total Q minus 1. So, if I substitute 2 in here, we get 4 over minus 1 is 3. Then I can solve for the volume of the box and it's 1 3rd of the volume of the of the equivalent volume associated with the speaker stiffness. and that is 94.3 liters. So that's the the size of the box that we would design a closed box design to achieve that desired cube. for the speaker.