Why is 2L Used for Function Periods?

[matqkks]

Why do most mathematics literature use 2L for the period of a function? Is it related to heat equation with a rod of length L?

 

[pasmith]

Why do most mathematics literature use 2L for the period of a function? Is it related to heat equation with a rod of length L?

Having a rod of length 2L with ends at $\pm L$ instead of a rod of length D with ends at 0 and D makes the mid-point symmetry more obvious.

Also the period of the sine and cosine functions is $2\pi$ and $\frac{2n\pi x}{2L} = \frac{n\pi x}{L}$ is neater than $\frac{2n\pi x}{D}$.

 

[LCKurtz]

It may be as simple as noting for a general period, instead of $2\pi$ call it $2p$. It certainly makes the Fourier coefficient formulas easier to remember. And it's why I like to use $p$ instead of $L$ in such formulas.