The speed and attenuation of ultrasound propagation can be used to determine material properties and identify phase transitions. Standard ultrasonic contact techniques are not always convenient due to the necessity of using couplant, however, recently reliable non-contact ultrasonic techniques involving electromagnetic generation and detection of ultrasound with electromagnetic acoustic transducers (EMATs) have been developed for use on electrically conducting and/or magnetic materials. We present a detailed study of magnetic phase transitions in a single crystal sample of Gd64Sc36 magnetic alloy using contact and non-contact ultrasonic techniques for two orientations of external magnetic field. Phase diagrams are constructed based on measurements of elastic constant, the attenuation, and the efficiency of generation when using an EMAT. The EMATs are shown to provide additional information related to the magnetic phase transitions in the studied sample, and results identify a conical helix phase in Gd64Sc36 in the magnetic field orientation H||c. ; Comment: 7 figures, 16 pages