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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?

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    $\begingroup$ "If an electromagnetic wave travels across a vacumm, isn't it pretty much invisible to the naked eye" Not unless it is in the visible spectrum. Are you asking about a specific scenario (like how would one test the frequency of EM waves in a microwave oven)? Or are you wondering more generally, like how do we think about and classify EM waves based on frequency? $\endgroup$
    – BioPhysicist
    Jun 8 at 17:41
  • $\begingroup$ Welcome randomHighSchooler! You may want to take a look at this related question: How do you measure wavelength/frequency of light $\endgroup$
    – Amit
    Jun 8 at 17:44
  • $\begingroup$ Here's one way to do it: web.physics.ucsb.edu/~phys128/experiments/interferometry/… $\endgroup$
    – vyali
    Jun 8 at 18:00
  • $\begingroup$ It is not invisible to the naked eye because after it travels through the vacuum it shakes the matter in the eye. $\endgroup$
    – Charles Hudgins
    Jun 9 at 1:56
  • $\begingroup$ Does this answer your question? How do you measure wavelength/frequency of light $\endgroup$
    – John Rennie
    Jun 9 at 4:14

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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.

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  • $\begingroup$ Measurement of optical interferometry is easily done in an undergrad physics lab. Direct measurement of optical frequencies (0.6 PHz) is getting closer if not already possible. We can buy off-the-shelf 0.4 Tb/s router AUI's, and that's limited by transmitter power rather than receiver capability. Given a known registration frequency (proven by its wavelength), using heterodyne/resonance-match frequency measurement in near ultra-violet is already possibe; see iopscience.iop.org/article/10.1088/1361-6455/ac8032/pdf $\endgroup$
    – Martin Kealey
    Jun 9 at 2:13

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