The evolution of the experimental frequency width of symmetric modes of an aluminum plate is studied as a function of the angle of incidence below the first critical angle. It is found that the frequency width predicted by resonant scattering theory, corrected for the directivity of emitter and receiver, generally explains the experimental frequency width well. However, large discrepancies remain for the frequency width of the S1 mode at angles of incidence larger than 9 degrees. It is demonstrated that these are caused by not taking into account the complex nature of the slowness of the plate mode. This suggests that there is a need for a theory that models the interaction of a beam of ultrasound, bounded in space and time, with an elastic plate.