THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

108 5. Vibrating BarsFigure 5.10. The tuning fork, essentially a U-shaped bar attached to a stem.out in a very short time, leaving only the pure sinusoidal fundamental, much inthe same manner as a xylophone. Because the stem shares the antinodal motionof the center of a free–free bar, the radiation efficiency of a tuning fork becomesgreatly increased by touching the stem to a surface of a large area such as acounter top.ReferencesFletcher, Neville H. and Rossing, Thomas D. 1991. The Physics of Musical Instruments.New York: Springer-Verlag, pp. 53–60.Kinsler, Lawrence E., Frey, Austin R., Coppens, Alan B., and Sanders, James V. 1982.Fundamentals of Acoustics, 3rd ed. New York: John Wiley & Sons, Chapter 3.Morse, Philip M. and Ingard., K. Uno. 1968. Theoretical Acoustics. New York: McGraw-Hill, Chapter 5.Reynolds, Douglas R. 1981. Engineering Principles of Acoustics, Noise and VibrationControl. Boston, MA: Allyn and Bacon, pp. 224–234.Wood, Alexander. 1966. Acoustics. New York: Dover Publications, pp. 384–386.Problems for Chapter 51. Show that a bar of length L, that is rigidly fixed at x = 0 and totally free atx = L will have only odd integral harmonic overtones.2. Determine the fundamental frequency of the bar in Problem 1 if L = 0.60 mand the bar is made of steel. If a static force F is applied to the free end, so