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Pentium100's answer is quite complete, but I'd like to give a much simpler (though less accurate) explanation.

The reason because sinewaves have (ideally) only one harmonic is because the sine is the "smoothest" periodic signal that you can have, and it's therefore the "best" in term of continuity, derivability and so. For this reason is convenient to express waveforms in terms of sinewaves (you can do it with other waves as well, as well as they are \$C^{\infty}\$).

Just an example: why in the water you usually see curved waves? (for this sake, ignore the effect of the beach or wind) Again, it's because it's the shape that requires less energy to form, since all the ramps and edges are smooth.

In some cases, like the Hammond organ, sinewaves are actually used to compose the signal, because with decomposition is possible to synthesize a lot of (virtually all) sounds.

There is a beautiful animation by LucasVB explaining the Fourier decomposition of a square wave:

These images explain better the square wave decomposition in harmonics:

Pentium100's answer is quite complete, but I'd like to give a much simpler (though less accurate) explanation.

The reason why sinewaves have (ideally) only one harmonic is because the sine is the "smoothest" periodic signal that you can have, and it's therefore the "best" in term of continuity, derivability and so on. For this reason it is convenient to express waveforms in terms of sinewaves (you can do it with other waves as well, as well as they are \$C^{\infty}\$, infinitely continuous and derivable).

Just an example: why do you usually see curved waves on water? (for the sake of the example, ignore the effects of the beach or wind) Again, it's because it's the shape that requires the least energy to form, since all the ramps are smooth.

In some cases, like the Hammond organ, sinewaves are actually used to compose the signal, because with decomposition is possible to synthesize a lot of (virtually all) sounds.

There is a beautiful animation by LucasVB explaining the Fourier decomposition of a square wave:

These images explain better the square wave decomposition in harmonics:

Pentium100's answer is quite complete, but I'd like to give a much simpler (though less accurate) explanation.

The reason because sinewaves have (ideally) only one harmonic is because the sine is the "smoothest" periodic signal that you can have, and it's therefore the "best" in term of continuity, derivability and so. For this reason is convenient to express waveforms in terms of sinewaves (you can do it with other waves as well, as well as they are \$C^{\infty}\$).

Just an example: why in the water you usually see curved waves? (for this sake, ignore the effect of the beach or wind) Again, it's because it's the shape that requires less energy to form, since all the ramps and edges are smooth.

In some cases, like the Hammond organ, sinewaves are actually used to compose the signal, because with decomposition is possible to synthesize a lot of (virtually all) sounds.

These images explain better the square wave decomposition in harmonics:

Pentium100's answer is quite complete, but I'd like to give a much simpler (though less accurate) explanation.

The reason because sinewaves have (ideally) only one harmonic is because the sine is the "smoothest" periodic signal that you can have, and it's therefore the "best" in term of continuity, derivability and so. For this reason is convenient to express waveforms in terms of sinewaves (you can do it with other waves as well, as well as they are \$C^{\infty}\$).

Just an example: why in the water you usually see curved waves? (for this sake, ignore the effect of the beach or wind) Again, it's because it's the shape that requires less energy to form, since all the ramps and edges are smooth.

In some cases, like the Hammond organ, sinewaves are actually used to compose the signal, because with decomposition is possible to synthesize a lot of (virtually all) sounds.

There is a beautiful animation by LucasVB explaining the Fourier decomposition of a square wave:

These images explain better the square wave decomposition in harmonics:

Pentium100's answer is quite complete, but I'd like to give a much simpler (though less accurate) explanation.

The reason because sinewaves have (ideally) only one harmonic is because the sine is the "smoothest" periodic signal that you can have, and it's therefore the "best" in term of continuity, derivability and so. For this reason is convenient to express waveforms in terms of sinewaves (you can do it with other waves as well, as well as they are \$C^{\infty}\$).

Just an example: why in the water you usually see curved waves? (for this sake, ignore the effect of the beach or wind) Again, it's because it's the shape that requires less energy to form, since all the ramps and edges are smooth.

These images explain better the square wave decomposition in harmonics:

Pentium100's answer is quite complete, but I'd like to give a much simpler (though less accurate) explanation.

The reason because sinewaves have (ideally) only one harmonic is because the sine is the "smoothest" periodic signal that you can have, and it's therefore the "best" in term of continuity, derivability and so. For this reason is convenient to express waveforms in terms of sinewaves (you can do it with other waves as well, as well as they are \$C^{\infty}\$).

Just an example: why in the water you usually see curved waves? (for this sake, ignore the effect of the beach or wind) Again, it's because it's the shape that requires less energy to form, since all the ramps and edges are smooth.

In some cases, like the Hammond organ, sinewaves are actually used to compose the signal, because with decomposition is possible to synthesize a lot of (virtually all) sounds.

These images explain better the square wave decomposition in harmonics: