So in the last lesson we talked about speaker enclosure design generally and specifically, we talked about the design equations for the closed box design. this week, we're going to talk, or today I should say, we're going to talk about the ported speaker design and it's a little more involved obviously. the, the port itself will be reminiscent of the [UNKNOWN] resonator, and the mass of the air in the port will oscillate in combination with the mass of the driver that's in the speaker, but it can be used to really tune the characteristic to enhance the low frequency sound. You'll see how that, that comes together both I'll, I'll give you some sketches and examples to demonstrate it and then we'll also develop the design equations by the end of the lecture today we will compare the close box design with the ported design and view some of the designs tools that are available on the web to do that, And that will close out the examples that we'll be pursuing in terms of enclosure designs here in this course. So the final cabinet design we're going to consider is the ported or what's called the bass reflex speaker cabinet. we've talked about this a little bit before already. There are 2 primary Cabinet designs, of course, one being the closed box which we have here, the other being the ported, where basically it's just as desired, there's a port in the box that couples to the speaker transducer. You know there are a number of speaker design tools that you can obtain online for free, The exampled webpage below, if you follow, the link to the web browser, will take you to a design tool, and just for a second I will pull that up. that's A J Designer. But you'll see here there is a design tool for calculating basically the dimensions of your port. The volume of your box for a given speaker design. And you can even generate a graphical output of the frequency response. And we talked about this. All the details are here as you drag the mouse across the screen. So you know we'll come back to this in a little bit. but in the mean time let's, continue on with the discussion on the enclosure. So let's start by considerign a simple model for the ported speaker. So, what I've sketched here is what's called a 2-degree freedom system and if you look at the sketch, if you remember last week we had the transducer itself so I've got the method of speaker transducer here As well as the stiffness of the speaker, which is is the stiffness associated with the spider. And we talked about that in the transducer. Remember the box has a stiffness itself. but there's also a mass of the port. And we talked about this in analogy with the Helmholtz resonator. And the the mass of the air in the port will oscillate just like the mass of the speaker. But they're coupled, and they're coupled by the stiffness of the box. and there's, this is a 2 degree freedom system, and it effectively has 2 modes. You remember earlier we talked about room modes and Standing waves. And, and, we talked about the modes of a string. when you have, 2 masses, you will have 2 modes. not an infinite number, just 2. Um.and basically, they can either oscillate together. Or they c-, in the same direction. Or they can oscillate. in opposite directions, okay? And there are 2 modes of oscillation that I'm going to show you below. let's focus on the, the motion of the speaker and the port being together. So in some sense they could. The masses could move back and forth together in unison as you see here by these vectors. In that case, it's almost as if the spring stiffness is just a very stiff rod and so you can just imagine the 2. masses moving up and down in this motion here, directly together as if they're rigidly attached. the alternative model or mode I should say, for them, is to mechanically move in opposite directions. So, As drawn here when this mass is moving in this direction, the mass of the port is moving in the opposite direction. conversely, just as we've sketched here, when the mass is moving back in this direction of the speaker transducer, the mass of the port is moving back in this direction. So that's the mechanical motion, so if you think about that, mechanically the masses is either move as if they are rigidly connected back and forth so they oscillate together or they move in opposite directions mechanically.