Step 2: The Circuit
For IC1 I used an LM358N dual operational amp. I prototyped the circuit using different op amps. They all worked, so use whatever you have in the parts bin.
IC1A is configured as a comparator. If the +input goes lower than the -input, the output goes low, which will turn on Q1. That is, if the resistance through the probes is less than 10 ohms (or any other value of R3) the output will go low.
IC1B is square wave oscillator. I got the circuit out of the LM358 app notes. As shown, the output frequency is around 1KHz. This can be varied by replacing R4 with a potentiometer.
When the transistor Q1 switches on, the output of IC1B (a 1KHz square wave) passes through the emitter, and switches Q2 on and off at 1KHz. The current from the collector of Q2 drives the speaker.
The emitter of Q1 originally drove a piezo transducer, but the results were not so good. Adding the power transistor Q2 gives enough current to drive a small speaker. The volume can be adjusted by replacing R9 with a potentiometer.
Build it. Use it. It makes a fine addition to any test bench.