A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
Wave Equation for Plane and Spherical Waves in Coherent Sound Fields
Plane or spherical waves would be fundamental wave modes. This chapter develops basic properties for plane and spherical waves from the perspective of phase characteristics on impedance functions. Pressure and velocity of plane waves could be in-phase; however, it may not be the case for spherical waves. A ratio of the two for a plane wave gives the specific impedance of a medium as a real number. A one-dimensional pipe exemplifies a correspondence between the geometric approach to discrete models and the wave theoretic formulation for continuous systems. The correspondence confirms the impedance functions for one-dimensional pipes may be minimum-phase. It may be not always a case in 3-dimensional systems for spherical waves. The inverse of minimum-phase function could be transformed into a causal function in the time domain. The transfer impedance for the pipe could be formulated by the wave theoretic approach assuming the inverse. Sound power output increases in proportion to the real part of radiation impedance of a source. Increasing only the real part, however, seems not be feasible, because the radiation impedance function for causal systems must be a complex function, in which real and imaginary parts are not independent.
Wave Equation for Plane and Spherical Waves in Coherent Sound Fields
Plane or spherical waves would be fundamental wave modes. This chapter develops basic properties for plane and spherical waves from the perspective of phase characteristics on impedance functions. Pressure and velocity of plane waves could be in-phase; however, it may not be the case for spherical waves. A ratio of the two for a plane wave gives the specific impedance of a medium as a real number. A one-dimensional pipe exemplifies a correspondence between the geometric approach to discrete models and the wave theoretic formulation for continuous systems. The correspondence confirms the impedance functions for one-dimensional pipes may be minimum-phase. It may be not always a case in 3-dimensional systems for spherical waves. The inverse of minimum-phase function could be transformed into a causal function in the time domain. The transfer impedance for the pipe could be formulated by the wave theoretic approach assuming the inverse. Sound power output increases in proportion to the real part of radiation impedance of a source. Increasing only the real part, however, seems not be feasible, because the radiation impedance function for causal systems must be a complex function, in which real and imaginary parts are not independent.
Wave Equation for Plane and Spherical Waves in Coherent Sound Fields
Tohyama, Mikio (author)
Phase Analysis of Sound Fields ; Chapter: 3 ; 67-94
2024-10-04
28 pages
Article/Chapter (Book)
Electronic Resource
English
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