How does a wave pass thru a medium?

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SUMMARY

A transverse wave passing through a medium, such as a rope, causes each particle to oscillate up and down between two extreme positions, creating crests and troughs. The particles do not all become crests and troughs in a sequential manner; instead, specific particles that reach the crest and trough positions during the first wavelength continue to oscillate in that pattern for subsequent wavelengths. This behavior is fundamental to understanding wave dynamics in physical mediums.

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khurram usman
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i mean i know particles move up and down but i want to go into a bit more detail.consider a constant fequency wave passing thru a rope.now what i want to know is that when the wave passes do all the particles bcome crest and trough turn by turn or do some specific particles (those which bcame crest and trough on the first wavelength) bcome crests and trough again and again after each wavelength?
kindly xplain
 
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Each particle reached by the wave oscillates up and down (for a transverse wave on a rope), between two extreme positions.
 

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