I've put together an lm386 audio amplifier circuit as shown in the image below. The volume was good when hooked up to the 9V output on my trainers breadboard, but when I hooked it up to a 9V battery, I couldn't get any sound out of it. I measured an 8V voltage drop when between the positive and negative end of the circuit on the breadboard and a 2V voltage drop with the same circuit powered by a 9V battery.
This makes me wonder where all the power is going (if not through the audio amplifier) in the battery-connected circuit. I am guessing that there is greater current from the breadboard, which pushes electrons through the circuit, but would like a more definitive answer.