Ultrasound wavefronts travelling through inhomogeneous materials such as biological tissues and tissue mimics are distorted by scattering processes. It has been proposed that measurements of these transmitted wavefronts may be used to define the contribution of coherent and incoherent scattering to the attenuation coefficient of such materials, by means of a comparison between the outputs of phase sensitive and phase insensitive receivers. Measurements of the complex pressure fields transmitted by scattering specimens consisting of glass beads in silicone rubber and by specimens of ox liver, kidney and myocardium have been carried out by point- by-point mapping of the amplitude and phase of the fields using a new design of pvdf needle hydrophone in a high precision scanning tank. It is demonstrated that transmission measurements of the scattered fields are not independent of the size and location of the measurement plane, and the proposed method is unlikely to be helpful in quantifying material properties. Alternative techniques based on the measurement of the angular scattering pattern of such materials are shown to be able to characterise scattering specimens consisting of glass beads in agar and gelatin, and to be able to distinguish normal ox myocardium from ox liver and kidney.