Attenuation of (n,o) Transverse Modes in a Rectangular Tube

The attenuation of (n,o) transverse modes due to heat conduction and viscosity at the walls of a rectangular tube can be calculated very simply by treating the tube as a duct whose side walls have a different admittance from the top and bottom walls. The (n,o) transverse modes may be represented as a sum of two plane waves at oblique incidence with respect to the side walls and at grazing incidence with respect to the top and bottom walls. Using Cremer's results for the wall admittance as a function of angle of incidence in conjunction with an extension of Morse's formulas for attenuation in rectangular ducts, an expression is found for the attenuation of all (n,o) tranverse modes; the dependence on the type of mode enters only through the cut‐off frequency, fc. This theoretical expression for the attenuation will be compared with the experimental results of Hartig and Lambert on (1,0) transverse modes.