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Now here's a question for everyone: Can a CD accurately represent a bona-fide square wave at say 15 kHz? Why or why not?
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No. Fourier series tells us you can represent a square wave as a sum of sinusoidal waves, but the frequencies required to reproduce a 15kHz square wave with decent fidelity will probably (I'm not going to do the math) run well into (and perhaps past) the MHz range.
Of course, that's if you were asking if a CD could
technically repoduce a 15kHz square wave accurately. If you're asking if it can
sonically (perceptually) reproduce a 15kHz wave accurately that's a bit more complicated. Numerous tests have shown that humans perceive high frequency waves and sine waves nearly identically. I say
nearly because there remains some debate on just how
near it really is. Suffice it to say that at the least, they sound very similar. And the reason is related again to the Fourier expansion of the square wave... we simply can't hear the frequency components that are part of the wave at much above 15kHz.