Measurements of newly defined intensimetric quantities and their physical interpretation

Abstract

This paper deals with the measurement and physical interpretation of the quantities a and r introduced in a previous paper ͓D. Stanzial, N. Prodi, and G. Schiffrer, ''Reactive intensity for general fields and energy polarization,'' J. Acoust. Soc. Am. 99, 1868-1876 ͑1996͔͒. The quantity a, which has the same time dependence as the squared acoustic pressure and the same direction as the time averaged sound intensity ͗j͘, will be called here ''radiating'' intensity, while r which has zero average, will be called ''oscillating'' intensity. A coherent picture of the energy transfer process in steady sound fields based on the decomposition jϭaϩr of the instantaneous sound intensity will be sketched and discussed. Furthermore, a direct experimental comparison between a and r and the real and imaginary parts of the complex intensity is presented for some field conditions.

Measurement of complex acoustic intensity in an acoustic waveguide

“…Accordingly, one needs to exercise caution when applying the method of Stanzial and Prodi 10 , especially in the study of the radiation of sound from complex noise sources, including, for example those noise sources studied in a later article 4 .…”

“…The definitions of Heyser 7 and Stanzial and Prodi 10 are principally of use in the study of instantaneous intensity. For a time stationary monochromatic sound field it is still possible to use these definitions by taking a time average of the instantaneous intensity; however, for non instantaneous intensity the definition of complex intensity is unambiguous and here it is usual practice to take a cross-spectrum between the measured sound pressure and particle velocity in order to compute the frequency dependent active and reactive intensity 1,19 .…”

“…Stanzial et al 11 also reinterpret the acoustic energy flow using an electrical analogy in order to define an acoustic power factor as the ratio of the active intensity to the complex intensity magnitude. The definition of complex intensity suggested by Stanzial and Prodi 10 is significantly different to that proposed by Heyser 7 , and so in this article the relative merits of each approach will be investigated. However, what is of most interest here is the use of Stanzial and Prodi's complex intensity definition in the study of sound radiation from complex noise sources.…”

“…A series of articles later introduce an alternative definition for instantaneous intensity in a general nonmonochromatic sound field [8][9][10] . In particular, Stanzial and Prodi 10 called these new parameters the radiating and oscillating intensities, which provide an alternative to the more usual active and reactive instantaneous intensity terminology. These definitions were chosen so that the time average of the radiating intensity equals the time average of the instantaneous intensity, and the time average of the oscillating intensity is zero.…”

“…Moreover, if one also studies a stationary sound field then the reactive intensity is likely to be significant over the entire length of the duct because both incident and reflected waves will propagate, so that one is not restricted solely to measuring close to a region of high modal scattering. Accordingly, this article begins in Section II by reviewing two methods of representing instantaneous complex intensity measurements, the methods of Heyser 7 and Stanzial and Prodi 10 . Here, use is made of a simple duct acoustics model in order to demonstrate some of the advantages and disadvantages of each method for the measurement of instantaneous intensity.…”