Thanks Studiot,
I'm comfortable with the electrical side of the equations (and I'm content to leave that as ILB). I'm more concerned with the developed pressure; which I don't know how to tackle properly.
As far as I can tell, a differential change in displacement \partial x creates a...
Thinking over it some more, I believe that the pressure in front of a non-enclosed moving membrane must be a velocity term, related to the diffusion equation.
The net result should be:
ILB=m\ddot{x}+\mu\dot{x}+\frac{2nRTx}{A(x^2-x_0^2)} for closed front, closed back...
I've been studying the behaviour of speakers and headphones for my own interest. I was able to derive the differential equation governing the motion of the speaker itself, what I've had trouble doing is deriving the pressure created by the speaker.
First the equation I've derived for...