jblisko / transmissionlossthroughwall

Solution to pressure wave equation with transmission loss of pressure through a wall, solved on a square domain.

TransmissionLossThroughWall

Solution using MATLAB to pressure wave equation with transmission loss of pressure through a wall, solved on a square domain. The purpose of this code is to emulate the effect of sound polution from roads near to someones home; more specifically, it modelled the placement of my college bedroom which was adjacent to a highway. The pressure is initialized as quiescent except the top and right boundaries, with a periodic magnitude condition using a sine function to vary the pressure on the boundary with the hope to make it more akin to having traffic on a road. We use a central-time-central-space discretization of the wave equation for the propogation of pressure in the following way: $$P_{i,j}^{n+1} = 2P_{i,j}^n - P_{i,j}^{n-1} + C^2 \left( P_{i+1,j}^n + P_{i-1,j}^n + P_{i,j+1}^n + P_{i,j-1}^n - 4P_{i,j}^n \right)$$ We note that we expressed our wave equation in a non-dimensional form $\partial_{tt}\overline P = \overline\nabla^2\overline P$, using dimensionless parameters $\overline P = P/P_0$, $\overline\nabla = L\nabla$, and $\overline t = (c/L) t$. The transmission loss through the wall is dictated by: $$TL = 10\log_{10} \left( 1 + \left( \frac{\rho_w h \omega}{2\rho_0 c} \right)^2 \right)$$ With the sound pressure level given by: $$SPL = 10\log_{10} \left(\frac{\langle P^2 \rangle}{P_{ref}^2} \right)$$ The results were compared against measured values within my apartment, with decent agreeance between the model and experiment.