I know this should be really simple but for some reason I'm having an absolute mental block.
I'm trying to determine the period and spatial frequency of the following function,
$ f(x) = \sum_{n=1}^{3} \frac{1}{n} \sin(\frac{nx}{a}) $
I know sine is periodic around 2$\pi$ so I assume $\frac{nx}{a}T = 2\pi $ and so $T= \frac{2\pi a}{n x}$, is this correct? I have a feeling that becuase the function dependent on $x$ we must first move it to the time domain to get its period. Am I being ridiculous
As for the spatial frequency, is it simply the inverse of this as usual?
$f = \frac{1}{T} = \frac{nx}{2\pi a}$
If someone could give me a slap and knock my undergraduate/high school maths back into me, I'd appreciate it