Superposition on longitudinal wave

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In a vibrating spring fixed at both ends, nodes occur where there is minimal displacement, while antinodes represent points of maximum displacement. The fixed ends of the spring create a pattern of reflection, leading to alternating regions of compression and rarefaction. During a complete cycle, maximum compression coincides with maximum rarefaction at different points. This relationship highlights that nodes and antinodes are positioned opposite to compression and rarefaction regions. Understanding this dynamic is crucial for analyzing 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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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