Inertial cavitation (IC) of the preformed microbubbles is being investigated for ultrasound imaging and therapeutic applications. However, microbubbles rupture during IC, creating smaller daughter bubbles (DBs), which may cause undesired bioeffects in the target region. Thus, it is important to determine the properties of DBs to achieve controllable cavitation activity for applications. In this study, we theoretically calculated the dissolution dynamics of sulfur hexafluoride bubbles. Then, we applied a 1-MHz single tone burst with different peak negative pressures (PNPs) and pulse lengths (PLs), and multiple 5-MHz tone bursts with fixed acoustic conditions to elicit IC of the preformed SonoVue microbubbles and scattering of DBs, respectively. After the IC and scattering signals were received by a 7.5-MHz transducer, time- and frequency-domain analysis was performed to obtain the IC dose and scattering intensity curve. The theoretical dissolution curves and measured scattering intensity curves were combined to determine the effect of the incident pulse parameters on the lifetime, mean radius and distribution range of DBs. Increased PNP reduced the lifetime and mean size of the DBs population and narrowed the size distribution. The proportion of small DBs (less than resonance size) increased from 36.83% to 85.98% with an increase in the PNP from 0.6 to 1.6 MPa. Moreover, increased PL caused a shift of the DB population to the smaller bubbles with shorter lifetime and narrower distribution. The proportion of small bubbles increased from 25.74% to 95.08% as the PL was increased from 5 to 100 µs. Finally, increased IC dose caused a smaller mean size, shorter lifetime and narrower distribution in the DB population. These results provide new insight into the relationship between the incident acoustic parameters and the properties of DBs, and a feasible strategy for achieving controllable cavitation activity in applications.