LennyB, nice find. That looks like a great Utube series.
The wire length will vibrate the most when it’s vibrating at the same frequency as the engine. That’s when it’s “blurred” and swinging the most as it has the most energy transfer from the engine to the wire. When the wire is vibrating the smoothest and most it’s the best match of the engine RPM.
Lengths of wire are calibrated to the dial speed RPM readout.
When vibrating the most that’s the resonant frequency and will be what they call vibrating in sympathy with the resonant frequency - the engine’s RPM speed and read out on the dial for that length of wire.
If you set the engine to 1800 RPM and got the wire to vibrate the most then set the engine to 3600 RPM the wire would have two vibrating waves and look like an 8 flattened out but very regular looking and smooth. The middle is called a node and does not vibrate so if you could put your finger on it your finger would not feel anything. The two waves at 3600 RPM would be showing the first harmonics of the 1800 vibration.
I’ve read a few times where the vibrating tachs were checked against pricy digital bench meters and read the same.
For setting an engine you can tape it to a snowblower and set the wire for 3600 then adjust the engine.