When an oak board is exposed to a change in the relative humidity of the ambient air, moisture transfer occurs. Consequentially, the internal moisture content distribution changes continuously, which induces bending of the board over time. With increasing asymmetry in the internal moisture content distribution, induced by an increasing difference in relative humidity over the board thickness, the board's curvature increases. In case the board is subjected to two different sinusoidal fluctuations in relative humidity on its opposite sides, the bending response is a superposition of two sinusoidal fluctuations. The influences of different fluctuation frequencies, amplitudes, and phase shifts on the macroscopic bending are theoretically predicted and experimentally explored. Moisture transport characteristics are derived from a frequency analysis of the macroscopic bending response, whereas the equilibrium bending configuration provides the linear hygroscopic expansion coefficient. Furthermore, the effect of hysteresis during sinusoidal relative humidity fluctuations is explored. The results are used in a case study to predict the deformation of an oak door separating an indoor and outdoor environment, with differently varying relative humidity on both sides of the door.