The pitch of the tone is dependent upon the resistance under test. The tester will respond to resistances of hundreds of kilohms, yet it is possible to distinguish differences of just tens of ohms in low-resistance circuits. Q1 and Q2 form a multivibrator, the frequency of which is influenced by the resistance between the test points. The output stage, Q3 and Q4, will drive a small loudspeaker or a telephone earpiece.
Simple-continuity-tester - schematic

The unit is powered by a 3-V battery, and draws very little current when not in use.

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