Eric B. Whiting

Initial laboratory experiments to validate a phase and gradient estimator method for the calculation of acoustic intensity

A recently developed phase and gradient estimator (PAGE) method for calculating acoustic intensity from multiple pressure measurements [Thomas et al., J. Acoust. Soc. Am. 134, 4058 (2013)] has been tested via anechoic laboratory measurements of the radiation from multiple loudspeakers. The measurements were used to examine the effects of probe geometry, size, frequency range, and source characteristics on the active intensity calculated from both the PAGE and the traditional cross-spectral approaches. Preliminary results are shown for multiple probe and source configurations, and confirm that the PAGE method results in a broader valid frequency range for a given probe geometry.

Performance of the phase and amplitude gradient estimator intensity method in interference fields

The phase and gradient amplitude estimator (PAGE) method improves the frequency bandwidth of estimated acoustic intensity over the traditional p-p method without altering the spacing between microphones [D. C. Thomas et al., J. Acoust. Soc. Am. 137, 3366–3376 (2015)]. For many broadband sources, accurate estimates may be obtained beyond the spatial Nyquist frequency by unwrapping the phase of a transfer function used in obtaining the phase gradient. However, inaccurate phase unwrapping in interference fields, such as those produced by two loudspeakers with equal strengths but opposite phase, has been observed. This results in erroneous intensity vectors. A two-dimensional, multi-microphone intensity probe was employed to investigate this phenomenon. Findings include: (a) the unwrapping error does not occur for all interference nulls, but is more likely to occur for deeper interference nulls where there is reduction in coherence; (b) rotation of the probe in the field alters which pair-wise transfer functi...

A comparison of different methods for calculating complex acoustic intensity

The Phase and Amplitude Gradient Estimation (PAGE) method of calculating acoustic intensity from multiple pressure measurements [Thomas et al., JASA 137, 3366–3376 (2015)] has been used successfully to calculate active intensity in the laboratory and in-field experiments. The primary result is that the PAGE method increases the bandwidth over which accurate vector intensity estimates can be obtained. Further work has investigated the application of the PAGE method to calculate other energy-based quantities, including the reactive intensity. Simulated pressure and particle velocity fields have been calculated for a single monopole, two out-of-phase monopoles, and, via Rayleigh integration, a baffled circular piston. The analytical intensity fields are then compared to the PAGE and the traditional p-p methods for obtaining both the active and reactive intensity, both in the near and far fields. [Work supported by NSF.]

Frequency dependence of slab coupled optical sensor sensitivity

This paper presents the frequency-dependent sensitivity of slab-coupled optical fiber sensors (SCOSs). This dependence is caused by the frequency characteristics of the relative permittivity. We show experimentally the frequency dependence of SCOS sensitivity for frequencies in the range of 1 kHz to 1 MHz for SCOS fabricated with both potassium titanyl phosphate (KTP) and lithium niobate (LiNbO(3)). We conclude that x-cut KTP SCOSs are preferred for measuring fields above 300 kHz as they are 1.55× more sensitive than x-cut LiNbO(3) SCOSs to the higher frequency fields. However, since KTP SCOSs experience increasing permittivity for low frequencies, SCOSs made with LiNbO(3) may be used for low frequency sensing applications due to their flat sensitivity response. For a 10 kHz electric field, an x cut LiNbO(3) SCOS is approximately 3.43× more sensitive than an x-cut KTP SCOS.

Three-microphone probe bias errors for acoustic intensity and specific acoustic impedance

In acoustic intensity estimation, adding a microphone at the probe center removes errors associated with pressure averaging. Analytical bias errors are presented for a one-dimensional, three-microphone probe for active intensity, reactive intensity, and specific acoustic impedance in a monopole field. Traditional estimation is compared with the Phase and Amplitude Gradient Estimator (PAGE) method; the PAGE method shows an increased bandwidth for all three quantities. The two- and three-microphone methods are compared experimentally, showing reduced bias errors with three-microphone PAGE for active and reactive intensity, whereas using two microphones is preferred for specific acoustic impedance.

Bias error analysis for phase and amplitude gradient estimation of acoustic intensity and specific acoustic impedance

Sound intensity measurements using two microphones have traditionally been processed using a cross-spectral method with inherent error in the finite-sum and finite-difference formulas. The phase and amplitude gradient estimator method (PAGE) has been seen experimentally to extend the bandwidth of broadband active intensity estimates by an order of magnitude. To provide an analytical foundation for the method, bias errors in active intensity and specific acoustic impedance are presented and compared to those of the traditional method. Bias errors are reported for a plane-wave field and sound radiated from a monopole and a dipole. Additionally, bias errors are reported for reactive intensity, the estimation of which is unchanged by the PAGE method for the two-microphone case.

Intensity-based laboratory-scale jet noise source characterization using the phase and amplitude gradient estimator method

A new method for the calculation of vector acoustic intensity from pressure microphone measurements has been applied to the aeroacoustic source characterization of an unheated, Mach 1.8 laboratory-scale jet. Because of the ability to unwrap the phase of the transfer functions between microphone pairs in the measurement of a broadband source, physically meaningful near-field intensity vectors are calculated up to the maximum analysis frequency of 32 kHz. This result improves upon the bandwidth of the traditional cross-spectral intensity calculation method by nearly an order of magnitude. The new intensity method is used to obtain a detailed description of the sound energy flow near the jet. The resulting intensity vectors have been used in a ray-tracing technique to identify the dominant source region over a broad range of frequencies. Additional aeroacoustics analyses provide insight into the frequency-dependent characteristics of jet noise radiation, including the nature of the hydrodynamic field and the...

Analytical intensity calculated from a wavepacket model and comparison to intensity measurements near a high-performance military aircraft

To create an equivalent source description of jet noise, a wavepacket model is used to determine the acoustic vector intensity away from the source. This paper represents an initial investigation into using the measured vector acoustic intensity to define wavepacket parameters. The complex pressure of a line source is defined according to an analytical hyperbolic tangent wavepacket model and Rayleigh integration is used to find the pressure, particle velocity, and time-averaged intensity at observer locations. The parameters that define the shape of the wavepacket are initially based on prior pressure level-based optimization carried out for ground-based microphones. The resulting calculated acoustic intensity vectors are compared to vector intensity measurements previously taken near a tethered high-performance military aircraft at military and afterburner engine conditions. The wavepacket parameters are then varied to provide an optimal fit using the intensity, rather than pressure level, as the cost fu...

Far-field acoustical measurements during a Space Launch System solid rocket motor static firing

Acoustical measurements were made in the very far field during a recent test firing of the five-segment QM-1 Space Launch System solid rocket motor at Orbital ATK. Data were taken using 6.35 mm and 12.7 mm type-1 microphones at three far-field locations to the sideline and aft of the nozzle at a range of 650–800 nozzle diameters. The experiment setup, including the appreciable terrain changes, is first discussed. Spectral and autocorrelation analyses highlight the variation of the noise with respect to observation angle. In addition, high-frequency spectral characteristics and waveform statistics are evidence of the significant nonlinear propagation over the propagation range. Effects of microphone size, terrain effects, and data stationarity during the firing are discussed. This dataset is compared to measurements of other solid rocket motors at closer and farther ranges, including the GEM-60 and the four-segment Shuttle Reusable Solid Rocket Motor.

Acoustical measurements during a static firing of the Space Launch System solid rocket motor

Acoustical measurements were made in the very far field during a recent test firing of the five-segment QM-1 Space Launch System solid rocket motor at Orbital ATK. Data were taken using 6.35 mm and 12.7 mm type-1 microphones at three far-field locations to the sideline and aft of the nozzle at a range of 650-800 nozzle diameters. The experiment setup, including the appreciable terrain changes, is first discussed. Spectral and autocorrelation analyses highlight the variation of the noise with respect to observation angle. In addition, high-frequency spectral characteristics and waveform statistics are evidence of the significant nonlinear propagation over the propagation range. Terrain effects and data stationarity during the firing are discussed. This dataset is compared to measurements of other solid rocket motors at closer and farther ranges, including the GEM-60 and the four-segment Shuttle Reusable Solid Rocket Motor.