# 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 '14 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. – Robert Mastragostino Jul 4 '14 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? – Ben Niehoff Jul 18 '17 at 14:57