Do you know how to explain how these work, or do you know where I might find someone who does? I want to build them with the HS physics class I’ve been given, but without understanding the workings, it seems more like a Scout project that was cool but taught very little. I’d even pay for tutoring on this, if I could really get my questions answered.
Here is an educational diode simulator for students to play with.
When I was a kid, circa 1987 back in India -I remember making a simple crystal radio. It consisted of a crystal diode (or whisker diode), the earpiece from an old telephone and the metal clothesline used by the family to dry clothes. Nothing else.
It worked great after sunset but only for the local radio station ( there was only 1). You connected two wires to the earpiece terminals and also connected the diode across the earpiece terminals. Then one of the wires was connected to the clothesline and the other one you bit down on 
Did you read the Wikipedia article? There is a fair amount of detail there about how they work, plus a large number of references and a “further reading” section.
In particular, look at this picture in that article, and the accompanying text:
That is an illustration of what the diode (modern day equivalent of the cat’s whisker) is doing for you. The rest of a simple crystal set is the tuner to pick up a specific carrier frequency (they don’t always have the filter capacitor to smooth the signal, as mentioned between b and c in that picture).
It’s always amazed me that the rectified signal with no amplification is powerful enough to drive a small headphone.
Well, Wikipedia has a pretty detailed explanation, but to summarize:
AM radio (crystal radios only work with AM) is a carrier wave that has the information you are sending encoded on it by varying the amplitude of the signal (hence Amplitude Modulation). The radio consists of an Antenna (to capture as much of the signal as possible), and turned circuit (to reject signals other than the one you are interested in), a crystal detector (to demodulate the signal), and a headphone (to hear the demodulated signal).
The crystal detector/demodulator converts the symmetrically-modulated carrier into a time-varying DC signal, which can be fed into the headphones and heard.
That diagram was burned into my head mumble years ago.
One thing to remember is that the radio waves are much closer together than the diagram shows. They are so close that after the signal is chopped in half, they tend to blur together well enough without any real filtering into a usable audio signal.
All you need is an antenna, something to tune with, something to rectify and something to listen with. The old cat whiskers or razor blade forms did the tuning/rectifying in one. A good crystal radio has an inductor and a capacitor for tuning (one being adjustable) and a silicon diode for rectification.
I had a RE kit as a kid that came with a ferrite core inductor with a screw adjustment*. Very fine tuning. With a long wire antenna I could get clear channel (note lower case) stations almost a thousand miles away.
Nowadays, you can’t get stations 50 miles away with a lot of consumer radios.
Pricey, though.
The fact that it’s an adjustable antenna, vs. just a tunable inductor, adds a lot I think.
Yeah, that’s a point worth mentioning - of course, if you were to draw it scale, they would be so close together it would obscure the point of the illustration. The signal gets filtered in that the headphone diaphragm can’t possibly move that fast. Although, people undoubtedly started sticking a small capacitor across the headphone leads because they perceived that it reduced static a bit.
AM radio is 535 - 1605 KHz. The upper limits of human hearing are general given as 20 KHz. That means that even if your hearing can pick that up, and the headphones attached to your crystal set could reproduce overtones up to that frequency (both doubtful), the carrier wave would be going through about 25 - 80 cycles for one cycle of the modulating wave. And the base frequencies of the tones you are listening to are MUCH lower - middle C on a piano is a bit over 250 Hz. The “plink” on the high end of the piano keyboard is about 4 KHz.