sign in sign up
<<
Home , Acoustics

Longwood University Digital Commons @ Longwood University

Chemistry and Faculty Publications Chemistry and Physics

4-2000 Blending History with Physics: Acoustic Charles D. Ross Longwood University, [email protected]

Follow this and additional works at: http://digitalcommons.longwood.edu/chemphys_facpubs Part of the Physics Commons

Recommended Citation Ross, Charles D., "Blending History with Physics: Acoustic Refraction" (2000). Chemistry and Physics Faculty Publications. Paper 26. http://digitalcommons.longwood.edu/chemphys_facpubs/26

This Article is brought to you for free and open access by the Chemistry and Physics at Digital Commons @ Longwood University. It has been accepted for inclusion in Chemistry and Physics Faculty Publications by an authorized administrator of Digital Commons @ Longwood University. For more information, please contact [email protected]. NOTE

Blending History with Physics: Acoustic Refraction Charles D. Ross, Department of Natural , Longwood College, Farmville, VA 23909; [email protected]

efraction is a traditional and ignored or given brief mention in on command decisions in the U.S. Rimportant concept in introduc- introductory texts. I would like here Civil War, but the phenomenon has tory physics courses. The basic ideas to point out that the study of been noted for several centuries. are often demonstrated through anal- is not only an excellent ogy and with ripple tanks, with sub- ancillary to the normal optical Outdoor Sound Propagation sequent discussion usually focusing approach, but also is rich in interdis- Outdoor sound propagation has on optical refraction. Mirages, ciplinary possibilities. The propaga- been studied extensively and there prisms, lenses, fiber , and rain- tion of sound outdoors has a signifi- are several excellent review articles bows all serve to illustrate the phe- cant historical context, especially in describing the phenomenon.1 What nomenon. warfare. My own research has been follows is a brief summary of the Acoustic refraction is usually directed towards the effects of sound main points. There are two primary reasons why a person close to an outdoor sound source will not hear sound from the source. First, matter between the source and potential receiver can interact with the sound in several ways. The total atten- uation of the sound (AT) is a combi- nation of three factors: geometric spreading of the wave AS, atmospher- ic AA, and extra attenua- tion AE, which groups together all other effects (for example: ground reflections, nonhomogeneity in the Fig. 1. Effects of wind shear on sound waves. atmosphere, and due to barriers, and scattering and diffraction due to atmospheric turbu- lence). The effects can be described by

AT = AS + AA + AE (1)

The second reason for inaudibility outdoors, and the focus of this note, is that the sound wave may be refracted due to wind or temperature effects. Normally, wind velocity increases with altitude (since frictional effects are less with greater altitude) and sound waves are refracted upward. Sound waves traveling in the same direction as the wind will be refract- Fig. 2. Long-range audibility and acoustic shadows resulting from acoustic refrac- ed downward by this wind shear. tion followed by ground reflections. Top of figure is a profile of emanating Thus, sounds tend to be heard more from a source in a temperature inversion; bottom part of figure is an overhead clearly at greater distances downwind view of the same situation.

208 THE PHYSICS TEACHER Vol. 38, April 2000 Blending History with Physics: Acoustic Refraction

Downloaded 12 Feb 2013 to 159.230.52.193. Redistribution subject to AAPT license or copyright; see http://tpt.aapt.org/authors/copyright_permission from the sound source than upwind. nications and military strategy in the This effect is shown in Fig. 1. 1860s, if a military commander inad- The lower atmosphere normally vertently placed himself in an exhibits a decreasing temperature acoustic shadow it often had disas- profile with increasing altitude, and trous consequences. Space does not sound waves refract upward (in much permit an extensive description of the the same way that light waves refract effects of unusual acoustics in the upward in the traditional mirage U.S. Civil War; the interested reader example). The in dry is encouraged to read previous articles air may be found from the following by the author (reprints available).3,4 equation: Here is a brief account of one of the various instances from that war. c (m/s) = 331.36 + 0.6067 T (2) At Iuka, Mississippi, on Sept. 20, 1862, Major General Ulysses S. where c is the speed of sound and T is Grant formulated a plan typical of the temperature in degrees centigrade. day, with sounds of battle acting as a A vertical temperature gradient of trigger for troop movements. His 10ЊC/km has the same refractive plan, if successful, would have effect as a vertical wind shear of brought about the defeat of one of the 6 m/s per km.2 For the idealized case primary Confederate armies (under of a constant sound-speed gradient, Sterling Price). Grant’s plan called sound waves will refract in a circular for forces under Brigadier General arc with radius R given by: William Rosecrans to come upon Iuka (where Price’s men were based) R = c0/G (3) from the south. The remainder of Grant’s men, under Major General where c0 is the sound speed at the Edward Ord, were to wait four miles source and G is the sound speed gra- north of Iuka until the sounds of dient. engagement between Rosecrans’s When the , forces and those of Price were heard. G, changes sign at a substantial Late in the afternoon, Ord and those interested in exploring the topic height (due to wind-induced down- Grant saw smoke rising from Iuka but more deeply will find a variety of ward refraction or from a temperature heard nothing and assumed that Price examples from both earlier and later inversion, with higher temperatures was burning supplies to prevent their periods (especially from World War aloft), sound waves can be refracted capture. Rosecrans and Price had I). back down to the ground. This sce- actually been engaged for over two nario can cause the sound to be audi- hours, but by the time couriers noti- References ble at some distance from the source, fied Grant it was too late: Price had 1. For example, see L. C. while observers closer to the source slipped out between the two Union Sutherland and G. A. Daigle, in hear nothing. The latter folks are said armies and avoided the intended pin- Handbook of Acoustics edited to be in an acoustic shadow zone. If cer movement. by M. J. Crocker (Wiley, New there is adequate ground reflection, The culprit in this case was a York, 1998), Chap. 28. the effect can repeat itself, causing a strong wind blowing from north to 2. R. G. Fleagle and J. A. “bulls-eye” pattern of rings of audi- south that had placed Grant and Ord Businger, An Introduction to bility and inaudibility around the in an acoustic shadow as sounds of (Aca- demic Press, New York, 1963), source (see Fig. 2). This effect can battle were refracted upward over p. 306. cause audibility of sounds of battle at their heads. unusually long distances: at times, 3. Charles Ross, “Shh! Battle in progress,” Civil War Times the battle of Gettysburg was inaudi- Comment Illus. 35, 56-62 (1996). ble ten miles away, while it was heard My students seem to find such clearly at times in Pittsburgh, 160 real-life cases of the effects of refrac- 4. Charles Ross, “Outdoor sound propagation in the US Civil miles (250 km) to the west. tion to be interesting and I encourage War,” Applied Acoust. 59, 137- others to try this interdisciplinary 147 (2000). An Example from the Civil War angle on an old topic. There are many Because of the of commu- such cases from the Civil War, and

Blending History with Physics: Acoustic Refraction THE PHYSICS TEACHER Vol. 38, April 2000 209

Downloaded 12 Feb 2013 to 159.230.52.193. Redistribution subject to AAPT license or copyright; see http://tpt.aapt.org/authors/copyright_permission