Electronic – Electronic stethoscope / contact mic not quite working

The LM386 amplifier's inputs are an internally biased differential pair, with common mode input range extending to the indicated ground, V_ee, or actually 0.4 Volts below ground.

In order to not disturb this internal biasing, the input signal must be capacitively coupled (or perfectly ground-referenced) - a capacitor in series on the input line is needed.

Next, for a voltage gain of 200, the input signal peak to peak needs to be under 1/200 of the output voltage range of the amp. While I could not find this specified in a quick scan of the datasheet, if we assume 7 volts output voltage range with a 9 Volt supply, the input signal needs to be under 35 mV peak to peak, to avoid clipping the signal. Clipping would result in mild to severe distortion of the output - though this does not explain the complete lack of signal you find on output.

If the incoming signal is higher than this 35 mV P-P, a potentiometer as an attenuator on the input is suggested.

Once these fixes are done, please revert with results, so the answer can be added to if needed.

Adding to @GeorgeHerold's answer:

1. You need to include frequencies down to below 30Hz. Most of the energy in a typical heartbeat is between 30 and 40Hz. Given the cutoff for the highpass that @GeorgHerold computed, you are losing a good 15dB at the lower end.
2. Try using a directional microphone instead of an omnidirectional. Directional microphones have two openings, one in front and one in back by the solder pads. I find I get much better results by installing a directional mic such that the front (where you normally speak into the mic) is inside the tube, with the port on the back of the microphone out in open air.

Actually, I don't use a stethoscope in my experiments. A simple plastic shell with a hole in it for the microphone works very well. What I've used for this is a plastic cap like you would use to close one end of a plastic water line. I had some laying around that are about 2" in diameter, and they work well.

I find that a directional electret microphone installed in a platic cap as described works well enough that I can capture heart sounds using nothing more than a PC or smartphone with no additional electronics - I can then do filtering, recording, or other processing digitally.
The PC soundcard has a 20dB boost on the mic input, but the smartphones don't. Since the cards use 16Bit sampling, you have plenty of headroom to digitally amplify the signal even without using the boost. If you resample from 44100 down to 400 or so, then you could probably gain the equivalent of a few bits