This Note describes a method to determine the viscous characteristic length $\gamma$ from an analysis and a linear regression of the dispersion curve. This approach is valid in the high frequency domain, above 20 kHz, where some asymptotic expansions simplify the theoretical equations. It is shown that there is a linear relationship between the squared propagation index and the inverse of the square root of the frequency which has a slope proportional to $\gamma$, the thermal characteristic length $\gamma'$ and some physical constants. The value of $\gamma'$ is determined using the Brunauer, Emmet and Teller (BET) method. Low frequency ultrasound, in the 40-200 kHz range, is used to perform the experiments. The computation of the dispersion curve from the experimental waveforms is done by using the phase spectrum method, as was outlined in a previous Note.