There isn't an engine-out sound in a Huey, just the rising tone from the squegging oscillator for low RPM, silenced by the solenoid on the mute switch.
Sometimes the generator can put a noise through the headsets, as can the strobe lights and the transponder - try turning each of these off in turn when all is running.
When your second noise comes through, and you used the mute switch, did it stay in the mute position? Because when the rotor RPM are in the normal range, you cannot make the mute switch stay in the mute position, being a solenoid.