Shock scattering histotripsy (SSH) involves a complex interaction between positive and negative phases of an acoustic burst to initiate a robust cavitation bubble cloud. To more precisely study these effects and optimize SSH therapy, we constructed a frequency compounding transducer to generate pseudo-monopolar ultrasound pulses. The transducer consisted of 113 individual piezoelectric elements with various resonant frequencies (250 kHz, 500 kHz, 750 kHz, 1 MHz, 1.5 MHz, 2 MHz, and 3 MHz). For each resonant frequency, a nearly 1.5-cycle pulse could be generated. Pseudo-monopolar peak positive pulses were generated by aligning the principal peak positive pressures of individual frequency components temporally so that they added constructively, and destructive interference occurred outside the peak-positive-overlapped temporal window. After inverting the polarity of the excitation signals, pseudo-monopolar peak negative pulses were generated similarly by aligning principal peak negative pressures. Decoupling the positive and negative acoustic phases could have significant advantages for therapeutic applications enhancing precision, avoiding cavitation at tissue interfaces, and reducing the acoustic aperture required for effective therapy. For example, we show that 16 SSH bubble clouds can be generated using only peak positive pulses following a single peak negative pulse. This results in a precise elongated lesion within red-blood-cell phantoms.