Is a Mechanical Wave Just a Sinusoidal Graph of Particle Motion?

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A mechanical wave is not merely a sinusoidal graph of a single particle's motion but represents the collective displacement of multiple particles, creating a wave-like pattern. The wave equation provides a mathematical solution that describes how these particles interact over time and space. While physics can model and predict wave behavior, it does not define the fundamental nature of what a wave "is." The philosophical implications of waves and their existence are left for further exploration beyond physics. Understanding waves involves both mathematical modeling and philosophical inquiry into their essence.
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What is a Wave?

Like,if i think of a particle doing a SHM, then i imagine a Particle going up and down continuously and its graph is a sinusoidal wave. But in case of Mechanical Waves, i am not really able to get the picture. Hence my question,

Is the Wave just a Sin Graph of a single particle or is it the way the particles displace themselves which in turn gives a wave like pattern?
 
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It's a solution to the wave equation. As for what it "is", physics can't answer that. It's a model, sure, but it happens to describe the very real phenomenon of anything which is a function of position and time like y(kx-vt). Philosophy must answer the rest, not physics.
 
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