On the apparent fractal dimension of sound bursts in acoustic signatures of two crunchy foods

The jaggedness of the filtered and compressed acoustic signatures of cheese balls and croutons at various levels of water activity was determined in terms of an apparent fractal (Kolmogorov) dimension. The plot of the mean dimension vs water activity had a characteristic sigmoid shape that could be adequately described by a modified version of the Fermi equation. Regression analysis yielded that the apparent fractal dimension, D-fK, of the cheese balls and croutons when dry was around 1.45 and 1.38, respectively. The inflection point, a(WC), that is, the water activity level where half the drop in D-fK occurred, was a(WC) = 0.50 and a(WC) = 0.55, respectively. The steepness of the jaggedness versus water activity relationship in terms of the a(W) range where about 90% of the drop of jaggedness occurred was 0.27 in the cheese balls and about 0.29 in the croutons.