# Why does a wall act as a low-pass filter?

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?

• Related question (but not a great answer imo): physics.stackexchange.com/q/18090/29216
– BMS
Jul 4, 2014 at 21:04
• The wall will internally stretch and compress for high frequencies, but not for low ones significantly wider than its thickness. This answer covers several aspects of the effects pretty nicely. Jul 4, 2014 at 22:54
• Think about this for a moment. You can represent the wall mathematically as a box potential; i.e., a function that is zero on $(-\infty,-a)$, then has a constant height of 1 on $[-a,a]$, then is again zero on $(a, \infty)$. Now, what is the Fourier transform of a box potential? Jul 18, 2017 at 14:57

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.