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

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san203
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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.