A power switch, an amplifying stage with some careful offsets, and a pitch-linear VCO driving an output transducer make a good continuity tester. The musical pitch of the tone produced is proportional to the resistance across the probe tips
Figure 1. A power switch, an amplifying stage with some careful offsets, and a pitch-linear VCO driving an output transducer make a good continuity tester. The musical pitch of the tone produced is proportional to the resistance across the probe tips