An ultrasonic interferometer for the characterization of the matter (solids, fluids & gases) in a medium is described, along with a method of using the same. The interferometer accurately determines the travel time of the multi-frequency ultrasonic signal in the matter that is being queried. By carefully selecting the design of the multi-frequency ultrasound signal, various properties of the material can be derived using a trainable classification system to classify or recognise the substance, or state of a process. The apparatus exploits the normally undesirable higher harmonics characteristics of the piezoceramic transducer to gain penetration through a spatial-frequency window that is not suitable for the higher frequency signals that are required to achieve the measurements.