In the recent work (Acoust. Sci. & Tech. vol.40, No.1 pp29-39 (2019)), we found with numerical study of a 2D flue organ pipe mode that the foot works as a Helmholtz resonator. When the frequency of acoustic oscillation in the pipe is higher than the resonance frequency of the Helmholtz resonator by almost the full-width at half-maximum, the most stable oscillation is observed, and the oscillation in the foot is anti-synchronized with that in the pipe. However, if the Helmholtz resonance frequency is nearly equal to the acoustic oscillation frequency, the oscillations in the pipe and foot become rather unstable and the oscillation in the foot lags behind that in the pipe by nearly pi/2. In this paper, we study the phase relations among the pressure oscillation in the foot, that in the pipe, and the hydrodynamic oscillation of the jet, which are the key to understanding the mechanism stabilizing and destabilizing oscillations of the flue organ pipe.