EFFECT OF FREQUENCY AND SPACE AVERAGING ON TRANSMISSION RESPONSES OF MULTIMODE MEDIA

Expressions for the standard deviation of the amplitude response of a multimode transmission medium to signals with nonzero bandwidth are derived. In the “statistical” case (normal modes overlapping frequency and negligible coherent transmission), the standard deviation is found to be approximately 5.57 (1 + 3.3âτW)â12 dB, where τ is the decay time constant of the energy of the normal modes and W is the bandwidth of the excitation signal. For spatial averaging, the standard deviation of the response fluctuation in decibels is approximately 5.57 (1 + 3.3X/⋔)â12 dB, where X is the length of the (linear) averaging interval and ⋔ is the wavelength of the excitation signal. For excitation signals with finite bandwidth W, the response fluctuations are given by 5.57[(1 + 3.3τW)(1 â 3.3X/⋔)]â12 dB, where ⋔ is the average wavelength. These results are applicable to fluctuation problems in multipath transmission, random vibrations, concert hall acoustics, and power measurements in reverberation chambers. © 1969, Acoustical Society of America. All rights reserved.