Natural Science Forum / Physics / Acoustics / February 2005

Hello to everyone,

I am measuring the complex wave number in an impedance tube, using a
configuration with three equally spaced microphone positions. It works quite
well for the real part, but I don't really know how to deal with the results
for the imaginary part (the damping coefficient).

When the complex wave number is k = w/c + j*beta, then beta represents the
damping coefficient. For the sound field in a tube, one can calculate a
theoretical value for beta, which takes only the thermal and viscous losses
at the tube walls into account. (The formula is given in ISO 10534, for
example). The results for beta are always positive values, the order of
magnitude is around 0.002 for Im(k)/Re(k) for our impedance tube.

When measuring the imaginary part of the wave number, I get values which are
both negative and positive. The absolute values are around Im(k)/Re(k) =
0.1, which are realistic values for an impedance tube, as I heard. My
problem is, that I don't know how to interpret the negative values for beta
that I measured. As I understood the whole thing, the damping coefficient in
a tube is a positive value, with the lower boundary determined by the
theoretical thermal and viscous losses (see above).

My results would look fine, if I just took the absolute values for the
imaginary part, but I don't really know if is as simple as that. Is there an
interpretation for a negative damping coefficient, or do you think these are
measuring errors? There may also be numerical errors in the calculation, as
you have to take the arccos of a complex value.

Thanks for any hints and best wishes,

Hannes Krummheuer
Student at Technical University Berlin