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ACOUSTICS OF TUNING FORKS
  Figure 6. A 426-Hz fork driven in its fundamental mode with an electromagnetic coil and a Microflown transducer (a) measures pressure and particle velocity in the near field at 7 cm from the fork (b) and in the far field at 80 cm from the fork (c). See text for explanation. Adapted from Russell et al., 2013, with permission.
  Figure 7. The Acoustical Society of America Gold Medal is the highest award of the Acoustical Society of America. The medal shows a tuning fork vibrating with a large displacement amplitude and radiating sound waves. Photo courtesy of Elaine Moran, used with permission.
 and the quantities are said to be in quadrature. Figure 6 shows measurements of the pressure and particle veloci- ties made with a matchstick-sized Microflown transducer
near a large 426-Hz fork. In the near field, at a distance of 7 cm from the tines, the pressure and particle velocity are seen to be nearly 90° out of phase to each other. But at a larger distance of 80 cm, in the far field, the pressure and particle velocity are nearly in phase. The quadrature phase relationship between pressure and particle velocity is a topic discussed frequently in upper level undergraduate and graduate acoustics courses covering spherical waves. However, even though I had known this for many years, as both a student and a teacher, the first time I obtained the experimental data in Figure 6 was an exciting moment.
The Tuning Fork on the Gold Medal of the Acoustical Society of America
The humble tuning fork is a simple mechanical device that is capable of demonstrating a wide variety of com- plex vibroacoustic phenomena. Perhaps it is no surprise that this marvelous acoustical apparatus is prominently featured on the Acoustical Society of America (ASA) Gold Medal (Figure 7), the most prestigious recogni- tion awarded by the ASA. It is interesting to note that the fork depicted on the medal appears to be vibrating with a sufficiently large amplitude so as to produce non- linearly generated integer harmonics. However, whereas the shape of the fork looks similar to those made by Koenig, the radiated wave fronts are far too close together (relative to the fork dimensions); this fork must have a fundamental frequency much higher than the 21,845-Hz fork in Koenig’s personal collection.
Acknowledgments
I thank my friend and former MS thesis advisor, Thomas D. Rossing, for introducing me to the fascinating acous- tics of tuning forks back when I was his student at Northern Illinois University, DeKalb.
References
Bates, L., Beach, T., and Arnott, M. (1999). Determination of the temperature dependence of Young’s modulus for stainless steel using a tuning fork. Journal of Undergraduate Research in Physics 18(1), 9-13.
Bickerton, R. C., and Barr, G. S. (1987). The origin of the tuning fork. Journal of the Royal Society of Medicine 80, 771-773. https://doi.org/10.1177/014107688708001215.
Blodgett, E. D. (2001). Determining the temperature dependence of Young’s modulus using a tuning fork. The Journal of the Acoustical Soci- ety of America 110(5), 2698. https://doi.org/10.1121/1.4777282.
Bogacz, B. F., and Pedziwaitr, A. T. (2015). The sound field around a tuning fork and the role of a resonance box. The Physics Teacher 53(2), 97-100. https://doi.org/10.1119/1.4905808.
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