Abstract: We present the experimental realization and theoretical explanation of a membrane-type acoustic metamaterial of very simple structure, capable of breaking the mass density law of sound attenuation in the 100—1000Hz regime by a significant margin (~200 times). Due to the membrane's weak elastic moduli, low frequency oscillation patterns can be found even in a small elastic film with fixed boundaries defined by a rigid grid. The vibrational eigenfrequencies can be tuned by placing a small mass at the center of the membrane sample. Near-total reflection is achieved at a frequency in between two eigenmodes where the in-plane average of the normal displacement is zero. By using finite element simulations, a negative dynamic mass is explicitly demonstrated at frequencies around the total reflection frequency. Excellent agreement between theory and experiment is obtained. We also show that the present mechanism can explain the phenomenon of total microwave transmission through subwavelength slits in metallic fractals, at frequencies intermediate between two local resonances.