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The Marginal Ice Zone (MIZ) forms a critical transition region between the ocean and sea ice cover as it protects the close ice further in from the effect of the steepest and most energetic open ocean waves. As waves propagate through the MIZ, they get exponentially attenuated. Unfortunately, the associated attenuation coefficient is difficult to accurately estimate and model, and there are still large uncertainties around which attenuation mechanisms dominate depending on the conditions. This makes it challenging to predict waves in ice attenuation, as well as sea ice breakup and dynamics. Here, we report in-situ observations of strongly modulated waves-in-ice amplitude, with a modulation period of around 12 hours. We show that simple explanations, such as changes in the incoming open water waves, or the effect of tides and currents and bathymetry, cannot explain for the observed modulation. Therefore, the significant wave height modulation observed in the ice most likely comes from a modulation of the waves-in-ice attenuation coefficient. To explain this, we conjecture that one or several waves-in-ice attenuation mechanisms are periodically modulated and switched on and off in the area of interest. We gather evidence that sea ice convergence and divergence is likely the factor driving this change in the waves in ice attenuation mechanisms and attenuation coefficient, for example by modulating the intensity of floe-floe interaction mechanisms.