Determination of in-duct sound power beyond the plane wave range using wall-mounted microphones

When studying the acoustic wave propagation in a duct, the frequency range can be divided into the low frequency plane wave range and the high frequency range with non-plane waves. In the low frequency range, the wave propagation is one-dimensional and the governing equations are rather simple. The larger the duct, the lower the frequency limit of the non-plane waves. Therefore, also taking into account the three-dimensional acoustic wave propagation is important, especially when considering the duct systems used in large machines. In practice often a harsh environment and immobile structures restrict the use of standardized noise measuring methods. For instance to characterize the exhaust noise of medium speed internal combustion engines (IC-engines) in situ, the in-duct sound pressures are measured using wall-mounted microphones. Then the low frequency range source sound power can be estimated by wave decomposition (``two-microphone method''). Often a three-microphone array is used to cover a sufficiently large frequency range. One way to formulate the sound pressure and sound power relationship in the high frequency range is to weight the sound pressures at the duct wall in one-third octave bands. The aim of this study is to extend the classical plane wave formulation by determining these weighting factors, so that a three-microphone array also can be used beyond the plane wave range. The results from numerical approach are compared to experimental data.