The ultrasonic measurements technique is well established to measure the elastic properties of rocks in the laboratory for seismic and well-log data interpretation. The key components of every laboratory ultrasonic setup are piezoelectric transducers, which generate and register elastic waves in rock samples. The elastic properties of rocks are determined through the velocities of elastic waves, which are measured by the times of the waves' travel from the source to the receiver transducer. Transducers can be specifically designed to generate P-waves (P-transducers) or S-waves (S-transducers). In limited studies, the measurement of P-wave velocities with S-transducers is mentioned. Such measurement is possible due to specific aspects of the operation of S-transducers. Namely, S-transducers are known to emit parasitic low-energy P-waves, which travel faster than high-energy S-waves and hence can be registered. However, no justification or elaboration of this method of measuring P-wave velocities was reported. To fill this gap, we first compare P-wave velocities measured with S-transducers against P-wave velocities measured with P-transducers in different rocks and materials. We show that the discrepancy between velocities measured with the two methods in homogeneous materials is less than 1% and can be up to 4% for natural rocks. Second, we numerically simulate the operation of S-transducers, show that parasitic P-waves have a dipole structure, and explain how the receiver transducer can register this compressional dipole. Finally, we use laser doppler interferometry to measure the displacement of the free surface of a sample caused by elastic waves emitted by the source S-transducer. We observed the dipole structure of the sample's surface displacement upon P-wave arrival on the surface.