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The frequency fluctuations of a single-frequency laser due to mechanical vibrations are dependent on the sound pressure and sound frequency. The two dependences have been studied with the observation of beat signals between two stable external-mirror He-Ne lasers in the free-running condition. The dependence on the sound pressure follows Hooke's law, so that the difference between the frequency fluctuations due to the acoustic noises and those due to the external vibrations was quantitatively distinguished. Some causes of mechanical instability of the laser were clarified from the dependence on the sound frequency as compared with the lowest natural frequencies of each mechanical element in the cavity. The translation of mirrors along the optical cavity axis and two rotations of mirrors about the axis perpendicular to the optical cavity axis, which give rise to the variation in the relative angle between the laser beam axis and the Brewster window plate, are the most dominant motions that cause frequency fluctuations of the laser.