The results of experimental and theoretical studies into the influence of ultrasound on the propagation of neutron waves in a thick Ge crystal are presented. The neutron intensity profiles were measured for the case of Laue diffraction inside the Borrmann fan. At low amplitudes of ultrasonic waves interference effects (diffraction intensity beatings) were observed. The observations were possible because of the uniform acoustic-field distribution through the whole bulk of the crystal. As distinct from the classical Shull experiments, wide analysing slits or position-sensitive detectors were used. To explain the results obtained, a modified theory for the spatial distribution of neutron diffraction intensities in the presence of acoustic excitation of the crystal is proposed. A good agreement between experiment and theory is obtained. At high amplitudes of ultrasonic waves the transition to kinematic scattering was not observed, despite the large strains in the crystalline lattice created by ultrasound. This could be connected with the formation of a superlattice having a standing wave period. A strong rise in the diffraction intensity and a sharp constriction of the neutron beam at the centre of the Borrmann fan were observed. This new effect could be used for the creation of ultrasound-controlled monochromators.