Electronic – Why does this potentiometer in an op-amp feedback path cause noise when adjusted

I think, if you assume that the internals of the op-amp contain, in effect, a first order low pass filter, you will have created for yourself what is known as a multiple feedback low-pass filter. I used a great simulation tool from Mister Okawa here to produce this: -

If you look closely at the circuit in the picture above and imagine that R2 and C2 are inside the op-amp, your circuit becomes the same. There is some hand-waving here because I'm taking a stab in the dark about what R2 and C2 actually are and "massaging" them numerically to fit close to producing a peak near 800 Hz.

C2 being 5pF is in the right order for the "conventional" stabilizing stage inside an old-fashioned op-amp like the TL081 and I guess R2 would be in the vicinity of a few kohm.

Anyway I'm convinced this is what is happening!!!

C9 is placed in the audio input path to block the DC that would otherwise flow because of the DC bias (~\$V_{CC} / 2\$) that will develop on the inverting input. A capacitor passes AC current and blocks DC current. The size of the capacitor determines how much AC at what frequency will pass through, that's why C9 is large-ish.

\$V_\text{CC}\$ doesn't come into it here. It powers the op amp, but doesn't connect directly to the op amp output. The DC portion of it that develops on the inverting input is blocked by C9.

The output capacitor blocks the DC in the output.

An ideal capacitor has infinite impedance at DC, which you can think of as AC having a frequency of zero. The capacitor's impedance (which is like resistance, except for AC) decreases as the frequency increases. Also measured in ohms, a capacitor's impedance is:

$$\frac{1}{2\pi fC}$$

Where \$f\$ is the frequency in Hertz (Hz) and \$C\$ is the capacitance in farads. 0.47uF seems a bit on the small side for low audio frequencies, so it might not have terrific low frequency response. The capacitor would have an impedance of ~17kΩ at 20Hz, for example, 1.7kΩ at 200Hz, etc. So about 1/3 of the input signal is dropped at 20Hz, about 1/30th at 200Hz. More may be dropped on the output depending on the impedance of the following stage.

The LM358 is a so-called "single supply" op amp, meaning it operates effectively with only a single voltage supply, \$V_{CC}\$ in this case. To do that, it "centers" the signal around half of the supply voltage. That's what the resistor divider on the non-inverting terminal is there for. So the output signal is AC superimposed on a DC value of say 6V for a 12V supply. That's why the output coupling capacitor is needed, to block the DC component, leaving only the amplified AC signal.