What Are the Different Dimensions of Sound and How Can They Be Distinguished?

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Peaweatherwax
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What is the nature of sound in each dimension e.d 1D, 2D, etc and how can one be differentiated from the other. I do not seek formulas just a straight forward explanation.
 
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Thanks jedishrfu, I did stumble upon that article but what I require is someone to explain that to me. :)