At the 145th Meeting of the Acoustical Society the authors presented a paper on the dispersion and absorption of sound in an idealized bubble field that had a bubble radius size distribution n(a) decreasing as the fourth power [J. Acoust. Soc. Am. 113, 1278 (2003)]. It was shown that, for this case, exact, relatively simple, analytic solutions exist both for dispersion and absorption. The same model is used here to calculate the effects of dispersion and absorption on pulsed signals as they propagate through a bubbly mixture. The approach is essentially the same as that used by Frank Henyey (unpublished) to analyze the propagation of signals through clouds that were observed in the well-known 1997 Scripps Pier experiment. The effects on signal shapes as a function of range and bubble density and size distribution will be presented.