Special Relativity. Lifetime.

[Alex K]

Nah, thanks to quantum theory, there is no fundamental difference between light and other particles, it's applicable universally. The frequency and time for a cycle are just the reciprocal of each other: 5 Hz means 1/5th of a second etc.

Hmm then again, perhaps frequency means different things depending on what it's describing. 5 Hz in neurons means they've fired 5 action potentials in the span of a second, but it does not mean each action potential lasts 1/5th of a second. To increase the frequency the time between firing decreases, but not how long each firing lasts.

Exactly, the frequency of 5 Hz would refer to the 5 times repetition of the entire cycle, not the length of any feature within this 0.2 second cycle. If you'd fourier decompose such a time dependent potential, what you'd find is a fundamental frequency of 5 Hz which takes care of the overall repetition ebery 1/5th of a second, and higher harmonics determining the shape of the potential. If the firing last much less than the 0.2 seconds of the overall cycle repetition, that just means that there are  lot of multiples of 5 Hz present in the spectrum shaping the signal.

Look:
your example would be the first picture, with f=5 Hz but relatively short pulses. Note how it therefore has some stronger and more higher harmonics at 10 Hz, 15 Hz etc. than the regular square wave in the second picture. The cosine wave has no higher components at all.