Compressions and Rarefactions in longitudinal waves

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SUMMARY

In longitudinal waves, compressions correspond to the highest displacement, analogous to crests in transverse waves, while rarefactions represent troughs. The relationship between compression and rarefaction is determined by the gradient of displacement, expressed as ∂u/∂x. For sinusoidal waves, maximum and minimum pressures occur at zero displacement, while pressure changes are zero at maximum displacement. An interactive animation demonstrates these concepts effectively.

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  • Familiarity with longitudinal and transverse wave properties
  • Basic knowledge of sinusoidal functions
  • Ability to interpret graphical representations of waves
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Students of physics, educators teaching wave mechanics, and professionals in acoustics or engineering fields interested in wave behavior and properties.

Ali_94
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I know this may seem quite trivial but I just want to make sure, do the compressions in a longitudinal wave represent the highest displacement, in a transverse wave this is known as the crest, and do rarefactions represent the equivalent of troughs in longitudinal waves?
Thank you in advance
 
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Yes, they do. You can send a longitudinal wave down a loooong spring and directly see alternate compression and expansion zones
 
In a longitudinal wave the amount of compression or rarefaction depends on the gradient of the displacement, \partial u / \partial x.

For a sinusiodal wave the maximum and minimum pressures occurs where the displacement is zero. The pressure change is zero where the displacement is a maximum.

See this animation: http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html - It's probably easiest to see if you set the "Form of tube" to "both ends closed". You can flip the graph to show either pressure or displacement.
 

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