In Search of the Missing Fundamental: by Richard K. Jones
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Lab 1

Objective:
By comparing the frequencies of the first four modes of an ideal circular vibrating membrane to those of a drum made from a dentists rubber dental dam and PVC pipe, the influences air-loading, membrane thickness and stiffness can be demonstrated.

Circular Membrane (drum head) Vibration
Video courtesy of  Dr. Dan Russell

A circular membrane (drum head) vibrates with a variety of interesting patterns and shapes, each at their own frequency. In this demonstration, a 6-inch square of latex rubber dental dam is stretched it over a short length of 4-inch diameter PVC pipe,and held  in place with rubber bands. Lines and circles are drawn on the membrane to help identify vibration shapes. A frequency generator  provides a sine wave to a loudspeaker. A strobe light was used to slow down the vibration so that it is easily visible. The flickering in this video is the result of mistiming between the strobe light and the video camera frame rate.

[CMV Drdanku]

Mode “Ideal” Ratio RDD Ratio
0,1 82.2 1F 82.2 1F
1,1 135.15 1.59F 158 1.92F
2,1 175.48 2.14F 217 2.64F
0,2 188 2.30F 227 2.76F

 

The above chart shows that the frequencies and subsequent ratios to the other modes of the latex rubber dental dam membrane differ from those of an ideal vibrating circular membrane if both had a fundamental frequency of 82.2 Hz.  Since the ideal membrane exists in theory only, the frequencies of the dental dam membrane have been affected by the thickness and stiffness of the membrane itself and to some degree, by the interaction between the membrane and the air inside of the PVC pipe and the air above the membrane. This interaction is referred to as air loading and significantly affects how larger membrane vibrates. Because of the small footprint, the membrane on the four inch PVC pipe is not affected by air loading to the same degree that a large timpani head would be, but it should be take into consideration.

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