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The propagation of acoustic disturbances in a porous medium crossed by numerous cracks (double porosity medium) is a complex problem that we here simplify by investigating the acoustics of a permeable channel. We consider a fluid-filled channel in two possible geometries, a slit or a cylindric pipe. The channel is surrounded by a porous medium (saturated with the same fluid) and is itself surrounded by an external medium. To simulate the average properties of the cracked rock, the external medium is either nonpermeable (few connections between cracks) or highly permeable (numerous connections). We present analytical and numerical results concerning acoustic disturbances of small amplitude generated in the channel, such as harmonic waves, step disturbanses and pulses.