Eigenmodes of a Room
Application ID: 63
When designing a concert hall it’s extremely important to take the resonances into account. For a clear and neutral sound, the eigenfrequencies should be evenly spread through the registers. For the home stereo owner, who can’t actually change the shape of his living room, another question is more relevant: where should the speakers be put for best sound?
To illustrate the effects we are going to calculate every eigenfrequencie below 100 Hz, together with their corresponding eigenmodes. The eigenmode shows the sound intensity pattern for its associated eigenfrequency. From the characteristics of the eigenmodes we can draw some conclusions as to where the speakers should be placed.
The eigenmodes differ slightly from the exact solution for an empty room. The equations are only solved in half the geometry and then analyzed everywhere using coupling variables.