New PDF release: Acoustics: Sound Fields and Transducers
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 special acoustical basics whereas including functional formulation and simulation tools.
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Additional info for Acoustics: Sound Fields and Transducers
For large values of kw, that is, for large distances or for high frequencies, Eq. 98) Zs z r0 c rayls: The impedance here is nearly purely resistive and approximately equal to the characteristic impedance for a plane freely traveling wave. In other words, the specific acoustic impedance a large distance from a cylindrical source in free space is nearly equal to that in a tube in which no reflections occur from the end opposite the source. 8 FREELY TRAVELING SPHERICAL WAVE Sound pressure. 99) where A~þ is the amplitude of the sound pressure in the outgoing wave at unit distance from the center of the sphere and A~À is the same for the reflected wave.
5 The wave equation in cylindrical coordinates The one-dimensional wave equations derived above are for plane-wave propagation along one dimension of a rectangular coordinate system. In the case of a line source, such as a vertical stack of loudspeakers in an auditorium, the sound spreads out radially in all directions as a cylindrical wave. To apply the wave equation to cylindrical waves, we must replace the operators on the left side of Eqs. 22) by operators appropriate to cylindrical coordinates.
First, at x ¼ l the sine curve must pass through the point u0. Second, at x ¼ 0 the sine curve must pass through zero. It is obvious that one and only one sine wave meeting these conditions can be drawn so that the amplitude is determined. Similarly, we could have chosen a frequency such that n ¼ 2, but where the length of the tube is slightly less than two half wavelengths. If this case had been asked for, the sine wave would have ended with a negative instead of a positive slope at x ¼ l. Sound pressure.
Acoustics: Sound Fields and Transducers by Leo L. Beranek, Tim Mellow