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

References 67medium. The time average E of e provides the energy density at any point in thefluidE = 1 T∫ T0edtwhere the time interval T represents one period of a harmonic wave. With the factthat p =∀ρ 0 cu, as manifested in Equation (3.32), Equation (3.61) becomese = ρ 0 u 2 = pu/cIf we now let p and u represent the amplitude of the pressure and particle velocity,respectively, then the time-averaged energy E is written asE = 1 2puc = p22 ρ 0 c 2 = 1 2 ρ 0 u 2 (3.62)For the cases of spherical or cylindrical waves or standing waves in a room, thepressure and particle velocity in Equation (3.61) must be the real quantities derivedfrom the superposition of all waves present. In these more complex cases, thepressure is not necessarily in phase with the particle speed, nor is the energydensity given by pu/2c. But E = pu/2c does constitute a good approximationfor progressive waves if the surfaces of constant phase approaches a radius ofcurvature much greater than a wavelength. This situation occurs for spherical andcylindrical waves at distances considerably far (i.e., many wavelengths) from theirsources.ReferencesFederal Register, May 28, 1975. v. 40: 23105.Federal Register, Oct. 29, 1974. v. 39: 38208.Federal Register, Oct. 30, 1974. v. 39: 38338.Harris, Cyril M. (ed.). 1991. Handbook of Acoustical Measurements and Noise Control,3rd ed. New York: McGraw-Hill, Chapters 1 and 2. (A most valuable reference manualfor the practicing acoustician.)Lord, Harold, Gatley, William S., and Evensen, H. A. 1980. Noise Control for Engineers.New York, NY: McGraw-Hill, pp. 7–30.Morse, Philip M. and Ingard, K. Uno K. Uno. 1968. Theoretical Acoustics. New York:McGraw-Hill. Chapter 1. (A classic text which probably contains more details thannecessary, with the result that the mathematics tends to obscure the physics ofacoustics.)Pierce, Alan D. 1981. Acoustics: An Introduction to Its Physical Principles andApplications. New York: McGraw-Hill, Chapters 1 and 2. (An excellent modern text bya contemporary acoustician.)