By Leo L. Beranek, Tim Mellow

ISBN-10: 0123914213

ISBN-13: 9780123914217

Acoustics: Sound Fields and Transducers is a completely up-to-date model of Leo Beranek's vintage 1954 ebook that keeps and expands at the original's specified acoustical basics whereas including functional formulation and simulation tools.

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**Extra info for Acoustics: Sound Fields and Transducers**

**Example text**

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. 9 The specific acoustic reactance (prms /urms) along the tube of Fig.

69) say that whenever kx is a small number the sound pressure leads by one-fourth period behind the particle velocity. At some other places in the tube, for example when x lies between l/4 and l/2, the sound pressure lags the particle velocity by one-fourth period. To see the relation between p and u more clearly, refer to Fig. 7 and Fig. 8, for the case of n ¼ 2. In Fig. 7, the particle motion is to the right whenever u is positive and to the left when it is negative. Hence, at x ¼ l/2, the particles on either side are moving toward each other, so that one-fourth period later the sound pressure will have built up to a maximum, as can be seen from Fig.

Integration of Eq. 68), after we have replaced u~ðxÞ by its value from Eq. 70) This result could alternatively have been obtained by setting ZT ¼ N in Eq. 58). 71) The pressure will equal zero at one or more planes in the tube whenever l is greater than l/4. Some examples are shown in Fig. 8. Here again, quantity n is equal to an approximate number of half wavelengths in the tube. Refer once more to Fig. 7 which is drawn for t ¼ 0. The instantaneous particle velocity is at its maximum (as a function of time).

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