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Nonlinear oscillations of bubbles can significantly increase the attenuationof the host media. Optimization of bubble related applications needs arealistic estimation of the medium attenuation and bubble activity. A correctestimation of the wave attenuation in bubbly media requires an accurateestimation of the power dissipated by nonlinear oscillations of bubbles.Pioneering work of Louisnard \cite{1} meticulously derived the nonlinear energyterms for viscous and thermal damping; however, radiation damping arising fromthe compressibility of the liquid was neglected. Jamshidi $\&$ Brenner \cite{2}have considered the effects of the compressibility of the liquid and showedthat damping due to radiation becomes the most significant factor at pressuresabove the blake threshold. Despite the improvement in their formulation;however, the radiation damping term estimates non-physical values for somefrequency and pressure regions including near resonance oscillations. Thus, thenew terms arising from the compressibility of the liquid needs criticalassessment. In this work, we provide critical corrections to the presentformulations. Importance of the new corrections are highlighted by thescattering to damping ratio (STDR). We then introduce a unifying parameter toassess the efficacy of applications; this parameter is defined as themultiplication of maximum scattered pressure by STDR.

Critical corrections to formulations of nonlinear energy dissipation of  ultrasonically excited bubbles and a unifying parameter to asses and enhance  bubble activity in applications