I like your approach with finding the frequency! I think the bit below the needle valve (between the green and the black handle) is most likely to be oscillating, as closing the needle valve ends the oscillation. I'm pretty sure it's a complex interplay between the components. We have a number of these "Sets" of valves, more or less the same design, but this is the only one that makes the noise. I think it's because the distance between the leftmost valves is bigger than in any other set.

I'm not sure how to measure what part is loudest. It isn't obvious when interacting with the pipe.

My first guesstimate is that the frequency is being generated at the junction above the left pipe. I think that the left pipe is resonating as what high school physics referred to as a closed pipe (closed at one end). The air flows through the junction, and the turbulence is such that it produces a tone.

We can test if I'm possibly right by measuring the length of the left pipe and doing some math

For discussion I am assuming that the left pipe is 0.5 meters long, and that average speed of sound is 343 m/s. Since I think this is like a closed pipe, we multiply the length by four. (Closed pipes resonate with only a quarter of the wave inside of the pipe).

Dorking around with an online tone generator (https://www.szynalski.com/tone-generator/ ), it sounds like it is roughly a 320 Hz tone.

speed of sound = wavelength * frequency
343 m/s = wavelength * 320 Hz
wavelength = 1.071875 meters
Pipe are often modeled as open or closed at one end. If it is open, wavelength / 2 = pipe length. If it is closed, wavelength / 4 = pipe length.
open: 1.07/2 = 0.5359 meters
closed: 1.07/4 = 0.2680 meters
I think that the pipe in resonance is more likely to be "open", because 0.5 meters looks like a length that is more likely to be present in the pipes. I think that by opening the valve on the left, a little more turbulence is introduced, and the turbulence excites oscillation between the junction and the middle pipe. I believe that this section, junction through middle pipe, is resonating as an open pipe, since it looks like it could be roughly 0.5 meters long.
If you want to test my idea, the pipe should be resonating loudest at the center between the junction and the end of the middle pipe. The junction and the end of the middle pipe themselves should be the nodes of the wave and rather quiet.