  The classical Blake threshold indicates the onset of quasistatic evolution
leading to cavitation for gas bubbles in liquids. When the mean pressure in the
liquid is reduced to a value below the vapor pressure, the Blake analysis
identifies a critical radius which separates quasistatically stable bubbles
from those which would cavitate. In this work, we analyze the cavitation
threshold for radially symmetric bubbles whose radii are slightly less than the
Blake critical radius, in the presence of time-periodic acoustic pressure
fields. A distinguished limit equation is derived that predicts the threshold
for cavitation for a wide range of liquid viscosities and forcing frequencies.
This equation also yields frequency-amplitude response curves. Moreover, for
fixed liquid viscosity, our study identifies the frequency that yields the
minimal forcing amplitude sufficient to initiate cavitation. Numerical
simulations of the full Rayleigh-Plesset equation confirm the accuracy of these
predictions. Finally, the implications of these findings for acoustic pressure
fields that consist of two frequencies will be discussed.
