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Calculation of acoustic intensity using the phase and amplitude gradient estimator (PAGE) method has been shown to increase the effective upper frequency limit beyond the traditional p-p method when the source of interest is broadband in frequency [Torrie, Whiting, Gee, Neilsen, and Sommerfeldt, Proc. Mtgs. Acoust. 23, 030005 (2015)]. PAGE processing calculates intensity for narrowband sources without bias error up to the spatial Nyquist frequency [Succo, Sommerfeldt, Gee, and Neilsen, Proc. Mtgs. Acoust. 30, 030015 (2018)]. The present work demonstrates that for narrowband sources with frequency content above the spatial Nyquist frequency, additive low-level broadband noise can improve intensity calculations. To be effective, the angular separation between the source and additive noise source should be less than 30 , while using phase unwrapping with a smaller angular separation will increase the usable bandwidth. The upper frequency limit for the bandwidth extension depends on angular separation, sound speed, and probe microphone spacing. Assuming the signal-to-additive-noise ratio (SNR a) is larger than 10 dB, the maximum level and angular bias errors incurred by the additive broadband noise beneath the frequency limit-or up until probe scattering effects must be taken into account-are less than 0.5 dB and 2:5 , respectively. Smaller angular separation yields smaller bias errors. V

The phase and amplitude gradient estimator (PAGE) method [Thomas etal., J. Acoust. Soc. Am. 137, 3366–3376 (2015)] has proven successful in improving the accuracy of measured energy quantities over the traditional p-p method in several applications. One advantage of the PAGE method is the use of phase unwrapping, which allows for increased measurement bandwidth. However, phase unwrapping works best for broadband sources and fields with high coherence. Narrowband sources often do not have coherent phase information over a sufficient bandwidth for a phase unwrapping algorithm to unwrap properly. Even for narrowband signals, the PAGE method has been shown to provide correct intensity measurements for frequencies up to the spatial Nyquist frequency. This is improved bandwidth over the p-p method. Previous work with sawtooth waves in a plane wave tube shows that in cases with multiple tones, the PAGE method with a few additional steps of processing accurately calculates intensity above the spatial Nyquist frequency provided one tone is below it. A variety of further experiments with multiple tones are explored to determine if any extra steps in processing or ingenuity in data acquisition can reasonably be used to achieve comparable results in a free-field environment. [Work supported by NSF.]

The application of implementing an active noise control system to globally attenuate noise radiated from a medical x-ray tube has been investigated. The noise radiated from the x-ray tube is characterized by the presence of numerous tonal peaks distributed over a broad frequency bandwidth. Furthermore, there is sufficient variability in the radiated field that coherence in the acoustic field was also found to be a challenge. It was determined that a properly placed structural sensor could be used as a reference signal to achieve good coherence between the reference signal and error microphone. In order to achieve global control, speakers were placed in close proximity to areas that had been identified as source regions through the use of SLDV and acoustic intensity measurements. The frequency band below 1500 Hz was targeted, and it was found that effective attenuation could be achieved at over ten of the most prominent frequencies, resulting in attenuations in that bandwidth on the order of 7 dB. Some of the challenges encountered and results obtained will be discussed and presented.

The phase and amplitude gradient estimation (PAGE) method [D. C.Thomas et al., J. Acoust. Soc. Am. 137, 3366-3376 (2015)] has proven successful in improving the accuracy of measured energy quantities over the traditional p-p method in several applications. For example, the PAGE method has successfully increased the bandwidth over which magnitude and phase calculations are accurate for broadband sources with smoothly varying phase. This is partially accomplished by unwrapping the phase relationship in order to get valid phase information above the spatial Nyquist frequency. However, narrowband sources may not have sufficient coherent bandwidth information for a phase unwrapping algorithm to unwrap properly. To test the limits of the PAGE method on narrowband sources, sine waves, sawtooth waves, and bandlimited white noise have been used in various scenarios. In one-dimensional tests of these signals, the PAGE method provides correct magnitude and direction for frequencies up to the spatial Nyquist frequency, which represents an extended bandwidth over the p-p method. Additional specific results for the different input signals are presented. Also presented are the results of using low-level broadband noise propagating in the same general direction as the source to provide sufficient information for accurate phase unwrapping. [Work supported by NSF.]