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There is not one clear answer to solve this problem. It would help to know the manufacturer and model number to analyze the system conditions. I heard this sound from many different brands of circulators and heard a similar sound from air conditioning coils.
The impeller, the circular part that spins to paddle the water, can move forward and back in the circulator body. As the circulator wears the bearing, or sediment builds on the body, flow conditions change. An impeller has several blades, the flow over it is not the same at all points around the circumference. As an impeller blade passes part of the pump head wall, the pressure at that point changes. The spinning impeller makes a rhythmic pressure wave in the water.
This hydraulic resonance is carried throughout the column of water instantly in all directions (Pascal’s Law,) as water is a non-compressible (it doesn’t take up shock like a gas.) A tube or pipe of the right size or diameter will act like a string in a guitar and vibrate sympathetically with the pulsations, so one possible solution is to fasten the vibrating section differently.
The pressure waves can become louder or go away as the impeller moves in the pump body (changing the vibration cavity or reed of a wind instrument changes the sound.) The sound might be reduced or made louder by changing the pressure conditions on the pump impeller. This might be done by changing the system pressure or changing the pressure against the impeller by shutting a valve slightly a few feet up the outlet pipe of the circulator (like blowing too soft or too hard on a clarinet.)
This is all really iffy. A quick fix might occur if you change the circulator. An experienced technician who will follow through this procedure until the noise disappears is your best solution.