I have a circuit that I want to be able to detect the frequency of the current going on it (part of the circuit is AC, the power supply is going to be at least 3v, probably 5v, and 6v DC at most). I don't need to know the exact numerical value of the frequency, just be able to tell when it changes to a different frequency. I have a very basic knowledge of electricity, so this may be a very overly simplistic interpretation of how it works, but could I connect the circuit directly to a small speaker, with a constant sound frequency indicating no change in current frequency (I imagine a constant hum), but with a change in the sound frequency (the hum becoming higher or lower pitched) indicating a change in the electric frequency?
Figure 1. (a) Simple test speaker. (b) Attenuator for PC speaker input.
Figure 1a might work adequately enough for you. C1 removes the DC component. R1 limits the current to a safe but possibly inaudible signal.
Figure 1b would allow you to plug into a set of computer loudspeakers with built-in amplifier. Start with the volume turned down.
Figure 2. gStrings for Android.
Many of the guitar or piano tuner apps have frequency readouts on them. Hold the phone up to the speaker and you can read the frequency.