where ρm is the measured density of porous PZT ceramics, D
is the diameter of the disc-shaped specimen, and fr is the
resonant vibration frequency. As shown in Fig. 8, the Z values
decreased almost linearly from 6.53 to 1.35 Mrayl with
increasing porosity due to the gradual introduction of air filled
pores into the ceramic matrix. The lowest value of Z was close
to that of biological tissue (1–2 Mrayl) or water ( ∼1.5 Mrayl),
which is beneficial in improving acoustic matching and helpful
for ultrasonic transducers application like hydrophone or
medical imaging. Meanwhile, there is no apparent discrepancy
in the dependence of acoustic impedance on porosity, which