Cassette tapes work by taking a plastic tape and coating it with something that can be magnetized. By changing the direction/strength of the magnetization, you can encode an analog signal on it. When that tape moves across a coil (the read head) the changing magnetic field induces a current in it. That creates the signal that is amplified and played as music.
The adaptor mimics this process by simply replacing the magnetic tape with a little electromagnet (coil) that the audio signal can be sent through. That looks to the read head just like a moving magnetic tape.
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