  We study the effects of atomic beams harmonic vibrations of micro amplitudes
and low frequencies on the mean atomic numbers of the detectors in atomic
Mach-Zehnder interferometer, where the two atomic beams are in the same wave
surface and have the same phases. We propose a vibrant factor F to
quantitatively describe the effects of atomic beams vibrations. It shows that:
(i)the vibrant factor F depends on the relative vibrant displacements and the
initial phases rather than the absolute amplitudes, (ii)the factor F increases
with the increase of the initial phases, and (iii)the frequencies can be
derived from equal time interval measurement of the mean atomic numbers. These
results imply that it is possible to detect the vibrations of micro amplitudes
and low frequencies by measuring the variations of mean atomic numbers.
