New experimental findings generic to the problem of transient wave transmission in periodic and random structures are discussed. Specifically, results are presented on the transmission of transient Rayleigh waves on grooved surfaces where the groove depth is small compared to a wavelength. These results, obtained using two‐dimensional ultrasonic models, reveal that, in direct contrast to continuous wave (cw) transmission, substantial energy can be transmitted along a grooved periodic surface at the Rayleigh wave Bragg frequency where the wavelength of the Rayleigh wave is twice the spatial wavelength of the grooved surface. The Bragg frequency energy arrives late over a wide time window. The transmission is characterized by a dominant main pulse followed by a ringing tail component. The spectrum of the main pulse has no major dips or peaks indicating that it is simply attenuated by the grooves (no discrimination against a specific frequency). Conversely, the spectrum of the tail portion for small grooves has a strong component near the Bragg frequency. The spectrum of the entire received signal has a dip at the ringing frequency indicating that the tail is out of phase with the main pulse. Shifts in the Bragg frequency occur due to the effects of topography on the Rayleigh wave velocity. Several different groove configurations are used to illustrate the effects of groove dimensions and spacing. Other results, obtained for unequally spaced grooves, show that destructive interference may eliminate the Bragg frequency ringing. The periodic grooves also initiate other Bragg frequency components associated with body waves and hybrid mode‐converted surface/body waves.