Superposition on longitudinal wave

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SUMMARY

The discussion focuses on the behavior of longitudinal waves in a spring fixed at both ends, specifically addressing the locations of nodes and antinodes. Nodes occur at points of minimal displacement, while antinodes are at points of maximum displacement. The relationship between compression and rarefaction is clarified, indicating that maximum compression coincides with maximum rarefaction over a complete cycle. This understanding is crucial for analyzing wave behavior in fixed systems.

PREREQUISITES
  • Understanding of longitudinal waves and their properties
  • Knowledge of wave mechanics, including nodes and antinodes
  • Familiarity with concepts of compression and rarefaction
  • Basic grasp of harmonic motion in fixed systems
NEXT STEPS
  • Research the mathematical representation of longitudinal waves
  • Explore the principles of wave reflection in fixed boundary conditions
  • Study the effects of varying tension on wave speed in springs
  • Investigate real-world applications of longitudinal wave behavior in materials
USEFUL FOR

Students and educators in physics, engineers working with wave mechanics, and anyone interested in the principles of wave behavior in fixed systems.

Kai
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When a spring is fixed at both ends and it is vibrating back and forth, reflection will occur. So where are the nodes and antinodes? Are they at compression or rarefaction region?
 
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Kai said:
When a spring is fixed at both ends and it is vibrating back and forth, reflection will occur. So where are the nodes and antinodes? Are they at compression or rarefaction region?
A node is where there is little or no displacement during a cycle, an antinode where the maximum displacement at that point is the maximum of anywhere. Since the ends are fixed, they will be ... which?
This is sort of opposite to compression and rarefaction. Compression and rarefaction regions can be found at some snapshot of the cycle, but over the course of a cycle they are the same places: maximum compression in one half of the cycle occurs where maximum rarefaction occurs in the other half.
These are maximised where displacement is minimised, and vice versa.
 

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