With a further generalization, we can consider losses that are dependent on frequency, so that the friction coefficient is replaced by . In such case, all the formulas up to (49) will be recomputed with this new .
Quite often, losses are deduced from experimental data which give the value . In these cases, it is useful to calculate the value of
so that the wave admittance can be computed.
From (33) we find
For instance, in a radius- cylindrical tube, the visco-thermal losses can be approximated by the formula 
In vibrating strings, the viscous friction with air determines a damping that can be represented by the formula