# Homework Help: Acoustic input impedance at ear entrance based on frequency and termination impedance

1. Jan 2, 2013

### pitchtwit

1. The problem statement, all variables and given/known data
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.

2. Relevant 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.

3. 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.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution