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Imagine 2 people each holding onto different end of a slinky and both of them starts synchronisation swinging up and down creating a standing wave also a transverse wave. But what about standing wave in longitudinal wave? I can only imagine pinching a spring between a thumb and index finger.

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Sorry, that was a bit terse.

http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/tralon.html#c1

Look at the diagram in the link. The point of a longitudinal standing wave is that a region of compression changes from compression to expansion but this pattern of compression and expansion does not move.

If you were to plot the density as a function of time, then at each point it would go up and down in a regular pattern, and the magnitude of the variation would be constant.

This makes the most sense in a linear medium where the wave can be viewed as a sinusoid. The definition of a standing wave becomes more difficult if the medium is non linear.

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