Why Does a Square Wave Contain Only Odd Harmonics?

[likephysics]

Why does a square wave contain only odd harmonics of the fundamental?
If the even harmonics are low, how low are they.
What happens to the even harmonics.

 

[LostConjugate]

Because the resulting function is odd. Even fundamental harmonics would be destructive.

 

[Andy Resnick]

Why does a square wave contain only odd harmonics of the fundamental?
If the even harmonics are low, how low are they.
What happens to the even harmonics.

That's the Fourier expansion for a square wave:
$$\frac{4}{\pi}(sin(x) + sin(3x)/3 + sin (5x)/5 + ...)$$

The function f(x) = |sin(x)| has only even harmonics.

 

[likephysics]

Does the duty cycle of the square wave have anything to do with the odd harmonics?