Okay. So, we've been talking about Helmholtz

resonators and bottles. And you're probably wondering now, what

in the world are we talking about bottles for if we're talking about audio and

music engineering. And in particular if we're interested

maybe in the design of speakers or cabinets for guitar amplifiers for

example, as we had discussed earlier. Well, it's pretty simple, and it's, it's

pretty significant. we're interested in the resonant

frequency of bottles. because for a closed speaker cabinet

design in particular, the stiffness of the cabinet is defined by the density rho

c squared speed of sound in air squared, the area, surface area associated with

the driver itself, okay. And so, if I put a speaker, a loudspeaker

driver in a box here. this is going to have a certain radius a,

okay. And then I can compute that surface area

as pi a squared there, and I end up with a stiffness in the box that's defined by

that surface area and the volume of the box itself.

Okay, so this basically ends up looking a whole lot like our discussion earlier on

the Helmholtz resonator. And that's why it's significant, because

we can now compute the stiffness of the cabinet as the function of the density,

the speed of sound squared, the volume of the box itself.

And the radius of the driver, the speaker component that you put in the box.

And this is, this part's important, because if you notice the, picking a

fixed volume for a box. So, keeping this fixed doesn't mean that

you have a fixed stiffness here, because it depends upon how large the driver is

that you choose to put in the box, and we can see that here.

and it varies significantly as a result of that because it's the area squared.

so changes in the radius can significantly affect the stiffness of the

speaker. Okay, I think that's enough with respect

to the intro on the on, on the, on the domain at resonance and how we hear.

And we will be working in our next lecture I think to talk a little more

about electronics and fundamentals of electronics.

And the next time I have a chance to speak with you we're going to talk a

little bit more about resonances in particular, and start relating that to

room acoustics.