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Bragg diffraction of atoms at thick standing light waves requires that the wave-matching condition is fulfilled. This usually means that the atomic beam crosses the light wave exactly at the Bragg angle. Nevertheless, our experiments also demonstrate Bragg diffraction at detuned angles if the amplitude of the standing light wave is temporally modulated with an appropriate frequency. If, on the other hand, the phase of the light wave is modulated no diffraction is observed. Both modulation processes produce frequency sidebands which set up `slowly travelling standing waves' in front of a retro-reflection mirror. Atoms are diffracted at these `almost standing' light waves in a similar way to photons at the travelling sound waves in an acousto-optic modulator. The frequency of the diffracted de Broglie waves is assumed to be shifted by the intensity modulation frequency. The different results using amplitude- and phase-modulated light waves are due to interference between the diffraction contributions of the individual frequency sidebands contained in the standing light wave.