Sine waves and 4th derivative and 4 dimensional space-time relationship?

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ThePhysicsGuy
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The 4th derivative of a sine wave is itself. This, of course, not only is a fact, but can be used to define the sine wave. My question is, are there any theories relating the abundance of sine waves in QM to the fact that the largest dimensions of space-time are together 4 dimensional? For example, I have often heard string theory explained as vibrating branes. Vibration tends to imply sine wave, so does string theory explain the causes of this vibration in terms of a 4th derivative being equal to the undifferentiated function?
 
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The answer to this question is no. String theory does not explicitly use the concept of a 4th derivative being equal to an undifferentiated function. Instead, string theory is based on the idea that the fundamental particles in nature are one-dimensional strings and that the dynamics of these strings can be described using quantum field theory. This is why the sine wave appears in quantum mechanics; it is simply an expression of the behavior of vibrating strings.