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:
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.