We present an experimental study and a model of the diffusion of sinuosidal pressure waves through porous media. We show that measurements of the hydraulic admittance A(ω) in the sine wave mode allow us to probe the structure of porous samples with an adjustable investigation depth depending on the frequency ω. The variations of A(ω) in heterogeneous media with a percolationlike geometry are modeled numerically on two-dimensional percolation networks. One obtains a transition from normal diffusion at low frequencies (‖A(ω)‖∝ω1/2) to anomalous diffusion at higher frequencies (‖A(ω)‖∝ω0.7). At the transition, the penetration depth of the wave is of the order of the percolation correlation length. The hydraulic admittance and transmittance of 20% porosity pressed calcite have been investigated experimentally with sine wave excitations at pulsations ω between 2¿10-4 and 0.42 rad/s. Both the modulus and the phase of the complex admittance A(ω) display normal diffusive variations as ω increases. Increasing the viscosity reduces the frequency above which the diffusive behavior is observed. The measured diffusion coefficient is 25% higher than that computed from permeability and compressibility values measured independently; this difference may be associated with nonconnected porosity. ¿ American Geophysical Union 1993<