Let’s take a look at the coil inductance.
A fun and easy place to start is look at some AC going through the coil (suggested in comments).
I used the oscilloscope’s test wave generator. I’m using two 10:1 probes connected thusly:
Channel 1 is shown above channel 2 on these oscilloscope screens:
Not much distortion at 500Hz:
At 50kHz we start to see some distortion:
At 500kHz we have obvious distortion:
Not sure what this tells us, but I’m sure it tell us something!
Now lets try a more abstract approach to the problem. We have a 6cm diameter air core coil with 60 turns. I found this handy inductance calculator. I looked up the thickness of 18 AWG wire and the relative permeability of air.
UPDATE: The rectangular function may be useful for calculating frequency.