PHY 221 Winter 2006 Syllabus and Flashcards
Research Interests:
Acoustic cavities formed by loudspeaker cones; The effect of loudspeaker
grills.
Recent research:
The effect of loudspeaker protective grilles (mainly automotive-related applications)
Those tricky acoustic waves that bounce around in front of loudspeakers and out toward our ears: How can we understand their complexity?: their relation to the loudspeaker cones that produce them? the room geometry, cabinet arrangements and even grilles which modify them?
Theoretically, they're described by the Helmholtz equation -- on the face of it, one of the simpler differential equations of physics. Still, solutions, predictive of the sound quality which we end up hearing, aren't easy to come by. Even when the motions of the loudspeaker cone are a simple "back and forth" and are the same at every point along the cone, the shape of the cone and the possible presence of a grille (which itself may be vibrating) can result in complicated sound patterns. Accordingly, approximate solutions are about the best we can do.
How approximate? Suppose we "guessed" the acoustic pressures at various points around the speaker's cone and in between it and the grille and then a bit farther out into the room. If we're right then not only is the Helmholtz equation satisfied but also the total energy stored in the acoustic waves will be minimized: changing any of our guesses would increase the energy. Since there are an infinite number of points at which the pressures are in question, the guessing method can't be used directly. This is where the finite element method comes in.
The finite element method is analogous to the way we interpolate between successively numbered dots on the kid's page of the sunday newspaper with a series of straight lines to make hidden shape appear. In the finite element method dots or "nodes" are connected to make a series of volumes which fit together like a three-dimensional jigsaw puzzle. Pressures guessed at the nodes are interpolated to create a 3-D picture of the pressures everywhere.
My Power Mac G3 finds the best guesses for pressures at 882 nodes in under 30 seconds -- no matter what the cone profile or grille openings look like. About 3000 lines of FORTRAN code does the job.
The first figure below shows a slice through the loudspeaker cone (the cone profile). The second figure is a graph of the sound pressure level in decibels at the ear (essentially the sound loudness) over a variety of frequencies at which the speaker (a 12 inch woofer in this case) might be expected to operate. The assumption used to get this data is that the maximum acceleration of the loudspeaker cone is the same at all frequencies, and that the listener?s ear is a meter away from the loudspeaker.
What I'm finding out from all this relates to the grilles used to protect the speakers -- how small can the holes be and still get good sound quality? Where best can what holes we do use be located? What about the effects of air viscosity and turbulence?
Figure 1: The vertical line at the left is the loudspeaker's symmetry axis - it extends out into the listening room pointing toward the listener's ear which is considered to be 1 meter away. The distance across the bottom of the figure represents a distance of about six inches. The grille occupies the next to bottom layer of finite elements; it has 23 very narrow more or less evenly spaced openings starting a little more than an inch from the center of the speaker at the lower left in the figure.
Figure 2: The response of this loudspeaker-grille combination.
And now back to Eastern Michigan University's Physics Department's Home Page or the PHY110 Home Page.