Understanding the Difference Between Modes and Nodes

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A mode refers to a specific pattern of vibration in a standing wave, characterized by its frequency and wavelength, while a node is a point in that wave where the medium remains stationary. In standing waves, nodes occur at fixed intervals, and the number of nodes helps determine the vibrational mode. Anti-nodes, in contrast, are points of maximum movement. Understanding these concepts is essential for analyzing wave behavior in various physical systems. The distinction between modes and nodes is crucial for studying harmonics and wave dynamics.
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Homework Statement


What is the difference between a mode and a node


The Attempt at a Solution


I am not really sure, because they seem exactly the same to me. Any help would be much appreciated!
 
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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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