  The problem of attenuation and sound speed of bubbly media has remained
partially unsolved. Comprehensive data regarding pressure-dependent changes of
the attenuation and sound speed of a bubbly medium are not available. Our
theoretical understanding of the problem is limited to linear or semi-linear
theoretical models, which are not accurate in the regime of large amplitude
bubble oscillations. Here, by controlling the size of the lipid coated bubbles
(mean diameter of ~5.4um), we report the first time observation and
characterization of the simultaneous pressure dependence of sound speed and
attenuation in bubbly water below, at and above MBs resonance (frequency range
between 1-3MHz). With increasing acoustic pressure (between 12.5-100kPa), the
frequency of the attenuation and sound speed peaks decreases while maximum and
minimum amplitudes of the sound speed increase. We propose a nonlinear model
for the estimation of the pressure dependent sound speed and attenuation with
good agreement with the experiments. The model calculations are validated by
comparing with the linear and semi-linear models predictions. One of the major
challenges of the previously developed models is the significant overestimation
of the attenuation at the bubble resonance at higher void fractions (e.g.
0.005). We addressed this problem by incorporating bubble-bubble interactions
and comparing the results to experiments. Influence of the bubble-bubble
interactions increases with increasing pressure. Within the examined exposure
parameters, we numerically show that, even for low void fractions (e.g.
5.1*10-6) with increasing pressure the sound speed may become 4 times higher
than the sound speed in the non-bubbly medium.
