By Leo L. Beranek, Tim Mellow
Acoustics: Sound Fields and Transducers is a completely up-to-date model of Leo Beranek's vintage 1954 booklet that keeps and expands at the original's designated acoustical basics whereas including useful formulation and simulation tools.
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Additional info for Acoustics: Sound Fields and Transducers
3 General solutions of the one-dimensional wave equation 35 or uðx; tÞ ¼ And from Eq. 0145 s, 1 407 uð5; tÞ ¼ 1 pðx; tÞ: r0 c 4e j628ðtÀ0:0145Þ þ 2e j1884ðtÀ0:0145Þ 4 j½628ðtÀ0:0145ÞÀðp=2Þ 2 j½1884ðtÀ0:0145ÞÀðp=2Þ : þ e e 628 1884 Taking the real parts of the two preceding equations, uð5; tÞ ¼ xð5; tÞ ¼ 1 ð4 cosð628t À 9:1Þ þ 2 cosð1884t À 27:3ÞÞ 407 1 407 4 2 sinð628t À 9:1Þ þ sinð1884t À 27:3Þ : 628 1884 Note that each term in the particle displacement is 90 out of time phase with the velocity and that the wave shape is different.
106) We can see that spherical waves differ from cylindrical ones in two respects: First, the radial wavelength remains constant as they progress, as is the case with plane waves. Second, although they decay in amplitude as they spread out, they adopt a direct inverse law in the far field. The latter makes sense when we consider that the area of the wave front is proportional to the square of the radial distance r. The radiated power is the intensity multiplied by the area, where the intensity is given by Eq.
64) or setting ZT ¼ N in Eq. 72) 44 CHAPTER 2 The wave equation and solutions p(x,t) (λ/2) t = T/4 t= n=1 3T 4 t = 0; T/2; T 0 x x=0 x=l p(x,t) 2(λ/2) 3T t= 4 n=2 t = T/4 t = 0; T/2; T 0 x=0 x x=l p(x,t) t = T/4 n=3 0 x=0 3(λ/2) 3T t= 4 t = 0; T/2; T x x=l FIG. , for three wavelengths. At x ¼ l, the rms particle velocity is u0, and at x ¼ 0, it is zero. The period T equals 1/f. 4 Solution of wave equation for air in a tube terminated by an impedance 45 −jZS = XS n=3 0 l′ = 0 x l′ = λ/2 l′ = λ l′ = l FIG.
Acoustics: Sound Fields and Transducers by Leo L. Beranek, Tim Mellow