Amplitude of particles in the medium of a longitudinal wave

[John Doe]

I was thaught you can create a sinusoidal wave by making a source oscillate with simple harmonic motion in a medium, such as moving one end of a rope up and down to create a periodic transverse wave. For transverse waves, it is easy to see that every particle in the rope moves up and down with (approximately) simple harmonic motion, with an amplitude equal to the amplitude of the wave itself.

¿Does the same principe apply to longitudinal waves? If you create a periodic longitudinal wave by making a piston or drum membrane move back and forth with simple harmonic motion ¿Will the air particles around it undergo simple harmonic motion, too? If so, wil they do so with the same amplitude as the source (the piston or drum membrane)?

 

[Orodruin]

A better analogy to your transversal wave would be a longitudinal wave in a spring as it is also a one-dimensional wave. Sound waves spread in three dimensions and their amplitude drops with distance as 1/r. This is true for both transversal and longitudinal waves.