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Sound Intensity and Its Measurement and Applications

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Sound Intensity and Its Measurement and Applications State of the Art of Sound Intensity and Its Measurement and Applications Finn Jacobsen Acoustic Technology, Ørsted@DTU, Technical University of Denmark, Building 352, DK-2800 Lyngby, Denmark The advent of sound intensity measurement systems in the beginning of the 1980s has had a significant influence on noise con- trol engineering. Today sound intensity measurements are routinely used in the determination of the sound power of machinery and other sources of noise in situ. Other important applications of sound intensity include the identification and rank ordering of partial noise sources, visualisation of sound fields, determination of the transmission losses of partitions, and determination of the radiation efficiencies of vibrating surfaces, and recent work suggests the possibility of measuring sound absorption in situ using sound intensity. This paper summarises the basic theory of sound intensity and its measurement and gives an overview of the state of the art in the various areas of application, with particular emphasis on recent developments. INTRODUCTION of the history of the development of sound intensity measurement is given in Frank Fahy’s monograph The most important acoustic quantity is certainly Sound Intensity [1]. the sound pressure. However, sources of sound emit The advent of sound intensity measurement sys- sound power, and sound fields are also energy fields tems in the 1980s has had a significant influence on in which potential and kinetic energies are generated, noise control engineering. Sound intensity measure- transmitted and dissipated. In spite of the fact that the ments make it possible to determine the sound power radiated sound power is a negligible part of the energy of sources without the use of costly special facilities conversion of almost any sound source, energy con- such as anechoic and reverberation rooms, and today siderations are of enormous practical importance in sound intensity measurements are routinely used in the acoustics. In ‘energy acoustics’ sources of noise are determination of the sound power of machinery and described in terms of their sound power, acoustic ma- other sources of noise in situ. Other important applica- terials are described in terms of the fraction of the in- tions of sound intensity include the identification and cident sound power that is absorbed, and the sound rank ordering of partial noise sources, visualisation of insulation of partitions is described in terms of the sound fields, determination of the transmission losses fraction of the incident sound power that is transmit- of partitions, and determination of the radiation effi- ted, the underlying assumption being that these prop- ciencies of vibrating surfaces. erties are independent of the particular circumstances. It is more difficult to measure sound intensity than This is not strictly true, but it is usually a good ap- to measure sound pressure. The difficulties are mainly proximation in a significant part of the audible fre- due to the fact that the accuracy of sound intensity quency range, and alternative methods based on linear measurements with a given measurement system de- quantities are vastly more complicated. pends very much on the sound field under study. An- Sound intensity is a measure of the flow of acous- other problem is that the distribution of the sound in- tic energy in a sound field. More precisely, the sound tensity in the near field of a complex source is far intensity I is a vector quantity defined as the time av- more complicated than the distribution of the sound erage of the net flow of sound energy through a unit pressure, indicating that sound fields can be much area in a direction perpendicular to the area. Although more complicated than earlier realised. The problems acousticians have attempted to measure this quantity are reflected in the extensive literature on the errors since the early 1930s it took almost fifty years before and limitations of sound intensity measurement and in reliable measurements could be made. Commercial the fairly complicated international standards for sound intensity measurement systems came on the sound power determination using sound intensity, ISO market in the beginning of the 1980s, and the first in- 9614-1 and ISO 9614-2. ternational standards for measurements using sound The purpose of this paper is to give an overview of intensity and for instruments for such measurements the status of sound intensity measurement, with em- were issued in the middle of the 1990s. A description phasis on developments from the past few years. MEASUREMENT PRINCIPLES AND mismatch errors ranging from 0.05° below 250 Hz to THEIR LIMITATIONS 1° at 5 kHz, which is slightly less than the maximum values specified in the IEC standard. There are essentially three methods of measuring It can be shown that the effect of a given phase sound intensity: i) one can combine two pressure error is a bias error that is proportional to the mean transducers (or more), ii) one can combine a pressure square pressure [7]. This implies that there is a limit to transducer with a particle velocity transducer, and iii) the amount of noise from sources outside the measure- one can use a microphone array. Each method has its ment surface that can be tolerated in sound power de- own limitations, but in addition there are some funda- termination using sound intensity, because such noise mental sources of error that do not depend on the mea- will invariably increase the surface integral of the surement principle [2, 3]. Array methods are used for mean square pressure and thus the bias error. reconstructing sound fields, including sound intensity. Another limitation of the measurement principle is This topic is outside the scope of this overview; see the restricted dynamic range at low frequencies: be- ref. [4]. cause the electrical noise of the microphones at low frequencies is amplified by the time integration need- ed in determining the particle velocity from the The two-microphone principle pressure gradient, one cannot in practice measure sound intensity levels below, say, 50 dB re 1 pW/m2 All sound intensity measurement systems in com- below 100 Hz [8]. mercial production today are based on the ‘two-micro- Other sources of error include the effect of air- phone’ (or ‘p-p’) principle, which makes use of two flow. Airflow gives rise to correlated noise signals closely spaced pressure microphones and relies on a that contaminate the signals from the two micro- finite difference approximation to the sound pressure phones. The result is a ‘false’ additive sound intensity gradient, from which the particle velocity is deter- at low frequencies [9]. mined. The IEC 1043 standard on instruments for the measurement of sound intensity deals exclusively with this measurement principle. The p-u measurement principle The finite difference approximation obviously im- plies an upper frequency limit. However, because of Attempts to develop sound intensity probes based the fact that the finite difference approximation error on the combination of a pressure transducer and a par- will be partially cancelled by a resonance if the length ticle velocity transducer have occasionally been de- of the spacer equals the diameter of the microphones, scribed in the literature [1]. A recent example is based the upper limit of the frequency range can be extended on the ‘microflown’ particle velocity transducer [10], to twice as much as suggested by the finite difference which is a micro machined hot wire anemometer. One error. Thus the resulting upper frequency limit of a problem with any particle velocity transducer, irre- sound intensity probe composed of half-inch micro- spective of the measurement principle, is the strong phones separated by a 12-mm spacer is 10 kHz [5], influence of airflow. Another unresolved problem is which is an octave above the limit determined by the how to determine the phase correction that is needed finite difference error when the interference of the when two fundamentally different transducers are microphones on the sound field is ignored [1]. An- combined (even though the influence of p-u phase other way of extending the frequency range is to apply mismatch will usually be less serious that the influ- a ‘sensitivity correction’ for the finite difference error. ence of p-p phase mismatch). Whereas one can com- Such a correction has recently been suggested for 3-D pensate for p-p phase mismatch by employing a simple intensity probes (without spacers) [6]; this also seems correction determined with a small coupler [7], there to double the upper frequency limit. is no similarly simple way of determining a correction Even with the best sound intensity measurement for p-u phase mismatch. systems available today the range of measurement is The measurement principle has the important ad- limited by small deviations between the phase re- vantage in sound power measurements that the perfor- sponses of the two measurement channels. Above a mance is not affected by the global pressure-intensity few hundred hertz the main source of phase mismatch index on the measurement surface, so in principle a is a difference between the resonance frequencies of larger amount of noise from sources outside the sur- the two microphones, which gives rise to a phase error face can be tolerated with p-u sound intensity probes that is proportional to the frequency. For example, one [11]. However, any such advantage has yet to be dem- must, with state-of-the-art equipment, allow for phase onstrated experimentally. APPLICATIONS Visualisation of Sound Fields Some of the most important applications of the Visualisation of sound fields, helped by modern sound intensity method are now discussed. computer graphics, contributes to our understanding of radiation and propagation of sound and of diffrac- Sound Power Determination tion and interference effects [16] and has stimulated much research on sound fields [4].
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