From my understanding, the frequency and wavelength of a mechanical wave can be observed by the motion of the particles (i.e., as the particles oscillate from their state of equilibrium, the wave propagates through the medium).
But, with electromagnetic waves, how do we measure its frequency and wavelength? If an electromagnetic wave travels across a vacuum, isn't it pretty much invisible to the naked eye?
Wavelength in the optical can be measured fairly easily with interference experiments, e.g. with a Michelson interferometer. We count the number of minima and maxima as we change the optical path length. The frequency for a given wavelength then follows indirectly from the formula $f=c/\lambda$.
There are more advanced ways of "counting" the frequency even for visible light, but they still require fairly advanced experimental techniques as far as I know. For microwaves (with wavelengths several hundred times longer than those of visible light) direct electronic frequency counting is relatively simple these days.
