A recent experimental investigation [Mazeetal., J. Acoust. Soc. Am.77, 1352 (1985)] has shown that the spectrum of the resonance frequencies of plates can be obtained using ultrasonic pulse techniques. The distortion of incident wave trains upon their reflection, when the carrier frequency is near a resonance frequency, is analyzed here; the physical origin of plate resonances can be elucidated, the observed ringing of the resonances being caused by multiple internal reflections. A series of backscattering experiments, employing wave trains with carrier frequencies on and off a resonance, has been interpreted in the mentioned fashion, with very good agreement between theory and experiment.