This week, we're going to talk a little bit about speaker cabinet design. we'll finish the lecture today with the closed-box design. but before we get into the specifics of how you actually design the enclosure, I'm going to spend a little bit of time talking about some of the basics. Even, even the sim, simple components of construction. and building a solid box will make a big difference in the quality of the sound. both in how it's constructed and how it's sealed. but I'd like to talk a little bit about the differences between, you know, a closed box design and ported design. And then, spend a little time providing you with the background to derive the design equations that are used in designing closed-box speakers. some of the math there's going to be beyond the requirements for this particular course. Don't get caught-up in it. I would just use that as an opportunity to think about, maybe some other courses you might like to take later. If you'd like to be able to do, to derive the design equations yourself. But not to worry, you'll be able to do, execute the designs independent of whether you can derive the equations or not. Okay. this week we're going to focus a bit on speaker cabinet design. And before we get into the design of closed-box speakers, which is what we'll consider first, I'd like to briefly discuss two of the primary cabinets. one being the closed-box speaker and the other being the ported or bass reflex speaker. you see, the difference between them is basically the port that's in the, the cabinet of the speaker. It allows the volume of air in the port to act in similar ways that the Helmholtz resonator did earlier. The mass of the air in that port oscillates and can enhance the sound radiation. But these are the two basic cabinet designs. there are other designs that include labyrinths and transmission lines. there's speakers that are far more complex to construct and tune and, and basically we're just not going to cover those in the context of this course. But you're more than welcome to look them up and do a little more reading on them. So, for now, we're going to focus on these two primary designs. the closed-box and the ported or bass reflex. Let's talk about the enclosure shape and design. Now, you know, we spent a good bit of time talking about room acoustics. and acoustics in three dimensions. this is an interesting case, because in this time, we're talking about the construction of a box that we're going to put our speaker in. we'd set that speaker box in a room. So but the, the box basically, the design of the box we can use some of what we learned in room acoustics to think about, how we choose, choose the enclosure shape. you'd never, you know, if we look at this top box here. You'd never want to pick an enclosure shape or design where the dimension, where one dimension is significantly greater than, than the other. so if, if you look at the, at, at the case here, actually, we have actually, it's Ly that's, three times Lx so this should be a y. I guess this should be x. But we wouldn't want to pick a design with a, with a an enclosure shape, like that. Because it'd behave like a resonant duct. And we already saw the the basic equations that describe that. But it at low frequency, it had very dominant standing waves, you know, along the length of the duct itself. And, and of course, that would give a, a, a very spiky response to the to the enclosure as a result. The other thing that to, to mention would be that we don't want to have a cube. so we really don't want an enclosure where, you know, Lx, Ly, and Lz are all the same. Now, why would that be the case, why do you think that would be the case? well, what happens is, is if you have a cube, the standing waves are going to be the exact same dimension in for each, the x y z dimensions. And my sketches here aren't great, but you get the point. So, and the resonant frequency associated with the standing wave in each of these predominant directions are all going to be identical. and that means they don't line up and they make the frequency response to the enclosure really peaky. Okay. So it turns out in enclosure design, a well established and a preferred dimension for the enclosure itself is based upon the golden ratio. And so a ratio of 0.618 to 1 to 1.618. and for the golden ratio, you can notice that 1 plus 0.618 is also equal to 1 divided by 0.618. basically, it provides a uniform distribtuion of the resonances in the enclosure. so there's the, the, the, the choice of that dimension actually, or the ratios of those dimensions ensures that you have, that the resonant peaks don't line up specifically to enhance each other at particular frequencies. It basically spreads them or distributes them across the the bandwidth more uniformly. All right. So, it's the least peaky of the design and you know, as I said before, the case where the, the, the natural frequencies you know, the 100, the 010 and the 001 modes, they don't equal each other. as an example. so, you really need to choose an enclosure that's based upon the parameters of the transducers that you use. as well as the desired frequency response of the speaker itself. and mainly the enclosure design is going to have the greatest impact at low frequency, that's where, you know, for the woofer or the low frequency driver. The box enclosures going to define some of the stiffness characteristics and really affect the response. The tweeters themselves, the higher frequency drivers relatively unaffected by the the box size or design. so before we discuss or focus on the options, it's probably worth providing a few guidelines for construction, generally. you, you know, I realize some of you may choose to build your own loudspeakers. I can tell you that it's that tuning of the speakers is far more tedious than you might anticipate when you first start the project. It's rewarding, I mean, and it's fun if you enjoy doing it, but the trick is, is recognizing that, you know, you're not going to just specify a few numbers in an equation and get something that sound phenomenal. If that were the case there wouldn't be any need to buy speakers. and there's typically some fine tuning that's required you know, the parameters of the speakers that you buy or the transducers aren't always perfect. And so, there's a lot of, you know, fine tuning and tweaking associated with that as well. but before we get to actually laying out the the speaker design, it's, it's really worth talking about a few things that are good guidelines in general construction. And one is, is that, you know, we put our high frequency drivers at the top of the cabinet. And our low frequency drivers at the bottom of the cabinet. the high frequency driver or transducer is typically referred to as the tweeter. And that should be placed closer to the plane or the ear. in terms of general construction rules too, I would also avoid the use of nails. screws are preferred over nails, for sure. And of course, glue and caulk are also frequently used to seal the cabinet. Here, I've shown, you know, basically a lap joint. in connecting the two sides of the cabinet. You could miter this. there's a lot of ways you can do it. You can strengthen it structurally. by putting a block here in the corner that you can attach, you can, you know, screw through to the to the block itself. You can glue that in the corner, but you generally want a really strong joint. And you want to make sure they're sealed, so that there's no air gaps. Otherwise, when the speakers vibrating, you end up with kind of a wheezing sound because you'll push air in and out of the cabinet, if there are any cracks or places where the air can leak. And that won't be and that would certainly won't enhance your sound radiation characteristics. so many options you can use to join the wood of the enclosure, and but, but again make sure it's a very rigid a rigid structure. It's also good advice to place some material in the box such as a foam or an insulation material, something that can absorb some of the reverberant sound in the box. you know, as I mentioned before the, the modes or the, the acoustic modes in the box or the enclosure itself inside will be fairly peaky. And if you if you if you add some absorptive material, it will cause that to decay out more quickly. And so, instead of having sorry, let me sketch on my sheet here. Instead of inside the box having a lot of frequencies that are, you know, that are peaky inside. You know, if I'm looking at the frequency response of the box. If you put some damping material in, some foam or something those peaks will round out. And so, they'll end up being flatter. not so sharp in terms of the in the in the enclosure themselves. But, you know, it's also important don't stuff the box full of materials because that will change the volume of the enclosure, and then it will effect the design and performance. So you know, just a small bit of lining, and maybe you can incorporate that into your estimate of the the volume of the box enclosure.