We analyze two seismic events that occurred on 27 May 2011 and 29 April 2013 at the Rocard submarine volcano which overlies the Society hot spot. The Polynesian Seismic Network recorded for the first time unusual associated short-and long-period signals, with perfectly monochromatic (0.0589 Hz) Rayleigh wave trains of long period and duration. None of the numerous observations of long-period (10-30 s) signals previously associated with volcanic activity in Japan, Italy, Mexico, Indonesia, Antarctica, and the Hawaiian Islands have the characteristics we observed at Rocard. We propose a tentative model for these unusual and rather enigmatic signals, in which the movement of lava excited the resonance of a shallow open conduit under a high hydrostatic pressure of similar to 400 bars.