I would like to know and understand more on Impedance Tube method to obtain on acoustical properties in formula term. It may very helpful to me, by proving the term in derive way. Thank you to all.
If you know the relative position of the 2 microphones, you can sum a propagating wave and a damped reflected wave at each position, with the phases of the waves shifted in regards of the mic position. Do that for the 2 positions and you get a system of 2 equations and 2 unknown amplitudes that you can solve.
Final equations are presented in both the ASTM and ISO norms.
I propose to situate the first microphone in node of standing wave and the second microphone in the "anti-node" of standing wave.
The ASTM normes ASTM E2611−09 and ASTM1050-12 describe the procedure to obtain the acoustics properties by using an impedance tube. A very good paper on the subject is : "Transfer function method of measuring in‐duct acoustic properties. I. Theory" J. Y. Chung http://dx.doi.org/10.1121/1.384778. This paper emphasises on the the theory and the experimental conditions : positions of the microphones and on the choice of the diameter and the length especially to obtain the low an high cut off frequencies desired. The paper focuses on the experimental conditions that ensure working with plane waves for accurately calculate the transfert function of the material under test. regards
Thank You Mr. Jacek Konieczny and Mr. Eric Rosenkrantz. great help for me. tq
You can look into this publication for theoretical derivation
https://pubs.aip.org/asa/jasa/article-abstract/68/3/907/776092/Transfer-function-method-of-measuring-in-duct
and this one for its experimental implementation
https://pubs.aip.org/asa/jasa/article-abstract/68/3/914/776090/Transfer-function-method-of-measuring-in-duct
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