wtorek, 19 sierpnia 2014

Acoustics absorption calculation (impedance tube)

Here is bunch of equations to calculate acoustic absorption coefficient according to transfer function method (ISO 10534-2:1998).
Absorption coefficient as function of frequency can be calculated from pressure reflection factor with:

Reflection factor is calculated from calculation (corrected) transfer function:
where 's' is microphones' spacing, 'x1' is distance form specimen to closer microphone and 'k0' is wave number.

Calculation (corrected) transfer function comes from:

Correction transfer function is obtained from:

and calculated as:

Please note that absorption coefficient calculation does not really need 'x1' distance to be known.
This is visible when following substitution is used in equation for reflection factor:

Then square of absolute value is given as (which is free from 'x1'):

Taking above into account ready to use equation can be derived:

taking following into account:

can be simplified to:


Note that calculations are a bit simpler using polar representation for complex numbers.

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