KE7GKP: Yes, at the moment, for testing purposes, I have it completely standalone from anything else. LM386 chip and the associated resistors and capacitors, that's all that's on the breadboard. Power is from a 9V battery. Pins 2 and 3 are both grounded. I have not tried taking it outside, I will look try that and see if there's any difference.
SurferTim: When I feed a signal to the LM386, it's plenty loud (at the 200gain) for my application. My concern is this noise I get out of the speaker when there is no signal at all (even when I disconnect the signal source and ground the LM386 input).
Generally, when there is a system such as this (signal source and amplifier) that is only used occasionally, does the amplifier remain on all the time? Or does one switch off the amp between uses? I keep thinking back to the PA system in my high school (15+ years ago) - when they were going to do an announcement, they'd switch it on, you'd hear a speaker noise (very similar to this if significantly louder), then the person would start speaking, then they'd turn it back off. Now obviously, that was turned on and off manually, but is there any reason not to set this up to switch off automatically? My signal source has a digital output pin that goes high whenever there's output, so I can pretty easily use that to control power to the amp. I'm wondering if this is appropriate design practice though...