Abstract: Properties of a medium, such as its particle size distribution, are characterized using a measurement cell containing a medium between walls of the cell, with ultrasound transducers on opposite walls. Ultrasound is transmitted from the ultrasound transducers on both sides and transmission and reflection responses are detected. An ultrasound frequency dependent ratio of a Fourier transform value of a product of signals obtained from transmission responses in opposite directions and a Fourier transform value of a product of signals obtained from reflections at the transducers is computed. Preferably, the first received reflected and transmitted pulses in response to pulse excitation are used to compute the ratio. Ultrasound frequency dependent ultrasound speed and/or attenuation data of ultrasound in the medium are computed as a function of the ultrasound frequency from the ratio. This eliminates the effect of the walls.