The collapse process of single bubbles in travelling bubble cavitation around two axisymmetric headforms have been studied acoustically to understand the collapse process of a cavitation bubble and characterize the sound emission in travelling bubble cavitation. The bubbles were observed to collapse and then sometimes to rebound and collapse again, resulting in one or two pulses in the acoustic signal from a cavitation event. It was observed that each of the pulses could contain more than one peak. This phenomenon is called multipeaking and is clearly distinct from rebounding. The occurrence of rebounding and multipeaking and their effects on some characteristic measures of the acoustic signal such as power spectra are examined in this paper. Two particular headforms (ITTC and Schiebe) with distinct flow characteristics were investigated.Both rebounding and multipeaking increased with reduction in the cavitation number for the ITTC headform. Smaller flow velocity, smaller cavitation number and multipeaking delay the rebound. The peak amplitude of the sound emitted from the first collapse was seen to be twice as large as the peak amplitude of sound from the second collapse, suggesting a repeatable process of bubble fission during the collapse process. Multipeaking and rebounding increased the characteristic measures of the acoustic signal such as the acoustic impulse. These characteristic measures have larger magnitudes for smaller flow velocity. Also, the values of these characteristics are larger for the ITTC headform than for Schiebe headform.Theoretical calculations based on the Rayleigh-Plesset equation were seen to correctly predict the order of magnitude of most of these characteristic measures. However, the distribution of spectral energy is not properly predicted; bubble fission during the collapse is thought to account for this discrepancy. Reduction in the cavitation number and multipeaking are observed to decrease the fraction of spectral energy contained in the high-frequency range (30-80 kHz).