We hope you are all looking forward to our December 4th lecture by Dr. Carol Reynolds on Music and Numbers. In case there are any doubts about the many rich connections between mathematics and music, Dr. Reynolds sent some excellent resources on Acoustics.
Dr. Dan Russell, a professor of applied physics, has used Mathematica software to visualize and explain complex acoustical phenomenon. Here for example is his explanation for one mode of a drum head vibrating:
The (0,3) mode, shown at right (MPEG movie ) has three circular nodes, but no diameter nodes. The frequency of the (0,3) mode is 3.598 times the frequency of the (0,1) mode. Like the (0,1) and (0,2) modes, the (0,3) mode is excited when the membrane is struck at the center. The sound radiation characteristics of the (0,3) mode rather complicated. This mode is excited when the membrane is struck at the center, and it dies away fairly quickly. As a result, it contributes to the “thump” sound when a drum is hit at the center, but does not contribute much to the musical pitch of a drum when hit off center.
These online multimedia lectures provide a great introduction to the physics of sound. Topics include oscillations, travelling waves, the Doppler effect, interference and standing waves. They also have articles specific to many of the instruments our students play: