## Tartini's Tone

- Details
- Category: Simulation and Modelling
- Last Updated on Thursday, 11 June 2015 12:57
- Written by Michael Berg
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# INTRODUCTION:

The program is a newly polished version of the macromechanical DPOAE-source demonstration. Interested users can download all the components from this zip file Berg_Tartini.zip. **IF you have a problem** (the zip file contains an exe file), please let us know and we will arrange another way ( the wetransfer service) of sending you the file.

The nucleus of the program goes back to **Jont B. Allen** and **Ekbert Deboer** long time ago, when computers were big, loud, hot and most expensive. (1k Core costed 1k Marks). The nonlinear concepts were added by the author. **Michael Ganz**, did some valuable supplements to reproduce “Margarete’s shoulder”, the Ldp=f(L1,L2).

The Program is written in Borland Pascal **under DOS**, easily movable to Borland Delphi 6 under Windows or Borland Kylix under Linux.

Who ever wants to know more, should not hesitate to contact the author by email at :
This email address is being protected from spambots. You need JavaScript enabled to view it.

HOW TO USE THE PROGRAM:

**Mac users can only use a simulation environment (Parallels, Virtual PC) to see the program running**. You can copy the file into a folder of your choice and then run it to expand its contents.

Once you expand the contents of the zip file , in the folder of your choice, you should see four files: (1) Tartini.exe ; (2) velo1.dat ; (3) velo2.dat ; and (4) velodp.dat. Run the executable program and then press the button "Read" (the first in the lower left corner), to Input the three data files. When this is done (takes 1 to 2 seconds) other buttons are activated. By pressing F1, or F2 you can see the waveforms of the two primaries. Pressing the 2F1-F2 generates the waveform of the cubic product non-linearity as shown in the **figure below**.

If you want to know the function of each button, place the cursor of the mouse over the button you want to identify its function, and a small explanation will be visible.**ADDITIONAL DETAILS:**

Nonlinear mechanics of the inner ear and its relation to otoacoustic emissions: two steps on the way to a mathematical model of DPOAE generation. Ganz M and Berg MF, Department of Experimental Audiology, University of Magdeburg, Germany.

Among clinical users of the registration of distortion product otoacoustic emissions (DPOAE), the understanding of the basic causality and interpretation of the phenomenon is not yet widely spread, nor is the expected influence of the middle ear and ear canal clear. On the other side, the effort in mathematical modeling of middle and inner ear structures is driven very far by now. We are convinced, though, that the essentials of an effect as DPOAE generation must be understandable from quite simple models. In a first step de Boer's one-dimensional model was adopted and expanded by a weak frictional and a weak elastic nonlinearity, respectively. By means of perturbation theory the weakly nonlinear problem is converted in an approximation series of linear problems. So it is solvable by the common methods of linear differential equations (DEs), above all the superposition principle can be used. At the same time a structure of causality is introduced: Sources for outgoing waves are in first order approximation formed by incoming waves, and so they can be localized. The calculations show clearly that of all six cubic distortions only the 2f(1) - f(2) term does have a source in its 'allowed' region and so can travel outward. We can use the calculated DPOAE to study the influence of middle ear, external ear canal and probe plug. Some problems remain: the weakly nonlinear model in first order does not give account for proper L(dp) = f(L(1), L(2)) and L(dp) = f(f(2)/f(1)) dependency, nor does it deliver additional sources or the effect of additional suppressor tones. In a second step, therefore, we replace de Boer's simple model basilar membrane (BM) by a doubly resonant, coupled tectorial/basilar membrane (TM/BM) system. By feedback now we introduce a strong nonlinearity, which we can mathematically care for by an iterative feedback loop. The algorithm shapes the incoming waves according to strong compressive nonlinearity. More relastic incoming waves yield better source terms, and after optimization of the mistuning function between TM and BM the model now is able to deliver qualitatively correct L(dp) (L(1),L(2)) and L(dp)(f(2)/f(1)) dependencies.

**A report on all is given in**:

Ganz M. (Magdeburg), Berg MF (Erlangen),
Nonlinear Mechanics of the Inner Ear and its Relation to Otoacoustic Emissions: Two Steps on the Way to a Mathematical Model of DPOAE Generation.
in Boehnke F (editor) Cochlear Mechanics, special issue of ORL, Karger, Basel 1999.

**ADDITIONAL REFERENCES:**

**Dr. Berg** has provided two additional text files with material related to the DPOAE generation program. These files include :

• An abstract on Otoacoustic Emitted Distorsion Products. A Clinical Study of Sudden Deafness Including Model Calculations for a Causal Interpretation of Disturbed Inner Ear Function. MD thesis presented to the Medical Faculty of the Friedrich-Alexander-Universitaet Erlangen-Nuernberg By **Margarete Maennlein-Mangold Erlangen**, April 1st 1998.

• The translation in english of his Appendix in the above thesis. The material is a very nice introduction to cochlear mechanics and it should be used easily by **graduate students** in Hearing Science.