Ultrasonic devices include a transducer having a piezoelectric element therein that may operate as an acoustic signal receiving surface and/or an acoustic signal generating surface. At least one acoustic matching layer is provided on the piezoelectric element. This at least one acoustic matching layer may be configured as a composite of N acoustic matching layers, with a first of the N acoustic matching layers contacting the primary surface of the piezoelectric element. This first acoustic matching layer may have an acoustic impedance equivalent to ZL1, where N is a positive integer greater than zero. In some embodiments of the invention, the magnitude of ZL1 may be defined as: 0.75 ((Zp)N+1(Zg))1/(N+2)≤ZL1≤1.25 ((Zp)N+1(Zg))1/(N+2), where Zp is the acoustic impedance of the piezoelectric element (e.g., lead zirconate titanate (PZT)) and Zg is the acoustic impedance of a compatible gas.