Up to now, low-frequency ultrasonic transducers have been manufactured using different materials and technologies and have been inspired by the biological world, mainly by the biosonar of dolphins and bats. Our research moves in this context, which is dedicated to investigating the feasibility of developing a piezopolymer sensor capable of covering the wide frequency range of a bat's biosonar. We propose an ultrasonic sensor manufactured using a sheet of polyvinylidene fluoride curved according to a logarithmic spiral geometry as it is present in biological models of the cochlea. Experiments were carried out both in transmission and reception, and demonstrated that a spiral-shaped transducer can transmit and receive ultrasonic signals similar to the specific vocalizations of most of the bats in the range between 20 and 80 kHz. The resonant frequencies of the transducer were evaluated through a finite element analysis, in agreement with experimental data covering the entire broadband. During transmission, the sound pressure level showed a maximum value of 90 dB, while during reception, the sensitivity spanned from t103.8 up to t89.1 dB. Directivity measurements demonstrated omnidirectional properties both on horizontal and vertical planes, representing a breakthrough in the field of broadband ultrasonic sensors.