By Leo L. Beranek, Tim Mellow
Acoustics: Sound Fields and Transducers is a completely up to date model of Leo Beranek's vintage 1954 e-book that keeps and expands at the original's designated acoustical basics whereas including sensible formulation and simulation tools.
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Additional info for Acoustics: Sound Fields and Transducers
3. 46) for pressure except for one important difference, which is the minus sign preceding p~À . The reason for this is fairly simple. During a positive pressure half-cycle, the resulting velocity is always in the direction of travel. Therefore, in the case of the wave with amplitude p~þ traveling in the positive x direction, positive pressure produces positive velocity because it is in the positive x direction, as shown by the dashed arrows in Fig. 3a. However, in the case of the wave with amplitude p~À traveling in the negative x direction, positive pressure produces negative velocity because it is in the negative x direction, as shown by the dashed arrows in Fig.
21. The “2” in parentheses denotes an outgoing spherical wave and the “1” denotes an incoming one. 11 Spherical coordinates 61 FIG. 20 Spherical Bessel functions of the first kind. FIG. 21 Spherical Bessel functions of the second kind. The inclination equation in q. After equating the right hand side of Eq. 156) Equating the left hand side of Eq.
115) For example, in the case of a plane wave with a direction of travel in the zx plane at an angle q to the z axis, we have kz ¼ k cos q, kx ¼ k sin q, and ky ¼ 0. The first bracketed term of Eq. 114) depends upon x only, while the second term depends upon y only and the third term z only. However, they must all add up to zero which means that either they all have constant values, the combination of which is zero, or they are all zero. We shall assume the latter, in which case Eq. 114) can be separated into three equations for each ordinate as follows.