The principle of electric guitar sensors directly applies Faraday's law of induction. Induced voltage Ui = -N*d(Phi)/dt. The magnetic flux is created by the permanent magnet of the sensor, the string is magnetically soft and changes the reluctance = magnetic resistance of the environment and thus creates changes in d(Phi)/dt.

https://www.youtube.com/watch?v=KKR-fdv0v-U

If you have an oscilloscope, you can demonstrate Faraday's law. With a lower frequency, the amplitude of the signal decreases as you tune the string. This is the effect of the derivative of the flux - the derivative is higher when the change is faster.

It is necessary to do this on one string. The sensor contains a magnetic pole for each string, which compensates for the different frequencies of different strings. Also, be careful of the electronics It is necessary to do this on one string. The sensor contains pole pieces for each string, which compensate for the different frequencies of different strings. Also, be careful of the built-in electronics in the guitar, which may contain a frequency filter and may mask the above error.