No, in longitudinal waves, particles of the medium do not move from one place to another; they simply oscillate back and forth about their position of rest.
Can particles of the medium in longitudinal waves move from one place to another?
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Yes, particles of the medium in longitudinal waves can move from one place to another. They oscillate back and forth in the direction parallel to the propagation of the wave, transmitting energy without causing permanent displacement of the medium.