Creating a Model of a Tube/Ear Canal in MATLAB

[pitchtwit]

Homework Statement

The context of this question is that it is the first question on a post grad paper in transducers and sound reinforcement. We've been looking at using electrical circuits to model acoustical and mechanical systems, and also using two-port analysis.

I need to create a model of a tube/ear canal using MATLAB, with facility to change the termination impedance to any known value. Termination is the ear drum and the acoustic input impedance is what I need to calculate/plot.
Info I have is that the ear canal can be assumed to be 30mm long, and as a first approximation may be considered as a cylindrical tube with a rigid termination. To start with I'm going to consider low frequencies only - allowing the lumped parameter model to be used, i.e. assume to reflections at openings.

Homework Equations

I need to know whether to use two-port analysis, or a mobility analog or impedance analog, and also whether changing the termination impedance means that the termination is no longer rigid.

The Attempt at a Solution

I tried using two-port analysis - using x=0 is the ear drum and x=-L is the opening. The matrix I used led to this result - (cos(k*L)+((1i*rho_0*c)/Z_0).*sin(k*L))./...
((1i/rho_0*c).*sin(k*L)+(1/Z_0)*cos(k*L));
which I've tried entering into MATLAB, but the results don't seem to make sense. For a start I know that the complex element of Z_neg_L should only be positive, and that it should not be at zero for so much of the time because when imag(Z_neg_L) is at zero that signifies resonance.

Any help would be greatly appreciated.

 

[mark726]

Thank you for sharing your question with us. It sounds like you are working on a very interesting project in the field of transducers and sound reinforcement. Based on the information you have provided, it seems like you are on the right track in terms of using two-port analysis to model the tube/ear canal system. However, it is important to carefully consider the assumptions and limitations of the lumped parameter model you are using.

In terms of the termination impedance, changing it may indeed affect the rigidity of the termination. This is something you will need to take into account in your model. Additionally, it may be helpful to use a more sophisticated model that takes into account the effects of reflections at the openings of the tube/ear canal.

As for the results you are getting in MATLAB, it is possible that there may be some errors in the equations or in the way you are inputting them. I would recommend double-checking your equations and perhaps seeking assistance from a colleague or mentor who is familiar with MATLAB and two-port analysis.

Overall, it seems like you are making good progress on your project and I wish you the best of luck in finding a solution. Keep in mind that it is always helpful to consult with others and to continue learning and exploring different approaches. Good luck!