Learning about the fourier transform and its connection to filtering/convolution got me curious about naturally occurring filters.
Why/how is it that brick walls naturally act as a low-pass filter (which requires something as seemingly complicated as convolution with the sinc function) to sound waves?
Any type of force waveform f(t) applied to the wall surface can be represented by the sum (integral if f(t) is not a periodic function) of sinusoidal vibration forces with different frequencies. Sound waves also cause physical forces on this air-wall boundary. This force creates the transmitted sound waves inside the wall. The sound wave attenuates as it propagates inside the wall where the amount of attenuation (per meter) depends on the attenuation constant which is - as you already said - is higher for the higher frequencies. The attenuation is expected to be higher if you try to vibrate the material faster, causing more frictions between the micro particles. This is roughly why it acts as a low pass filter.
Because the width of the typical internal wall cavity corresponds to the wave-length of low audio frequencies and their constituent harmonics.
