Penelope Menounou

Directive line source model: A new model for sound diffraction by half planes and wedges

A new method termed Directive Line Source Model (DLSM) is presented for predicting the diffracted field produced by a sound wave incident on a rigid or pressure release half plane. In the new method the edge of the half plane is modeled as an infinite set of directive point sources continuously distributed along the edge. Because DLSM is fast, simple and intuitive, it is a promising tool for the study of diffraction. It can be applied for several types of incident radiation: omnidirectional cylindrical and spherical waves, plane waves, as well as waves from directional sources. Wedges may also be treated. Finally, DLSM can handle diffraction by an arbitrarily shaped edge profile, for example, a half plane having an edge that is jagged instead of straight. Results for plane, cylindrical and spherical incident waves, as well as for arrays of line and point sources, are presented and their agreement with known analytical solutions is demonstrated. Predictions based on DLSM compare favorably with experimental data.

A new method to predict the evolution of the power spectral density for a finite-amplitude sound wave

A method to predict the effect of nonlinearity on the power spectral density of a plane wave traveling in a thermoviscous fluid is presented. As opposed to time-domain methods, the method presented here is based directly on the power spectral density of the signal, not the signal itself. The Burgers equation is employed for the mathematical description of the combined effects of nonlinearity and dissipation. The Burgers equation is transformed into an infinite set of linear equations that describe the evolution of the joint moments of the signal. A method for solving this system of equations is presented. Only a finite number of equations is appropriately selected and solved by numerical means. For the method to be applied all appropriate joint moments must be known at the source. If the source condition has Gaussian characteristics (it is a Gaussian noise signal or a Gaussian stationary and ergodic stochastic process), then all the joint moments can be computed from the power spectral density of the signal at the source. Numerical results from the presented method are shown to be in good agreement with known analytical solutions in the preshock region for two benchmark cases: (i) sinusoidal source signal and (ii) a Gaussian stochastic process as the source condition.

A correction to Maekawa’s curve for the insertion loss behind barriers

Maekawas curve is one of the most established methods for predicting the insertion loss (IL) behind barriers. For the simple case of a barrier modeled as a half plane, the IL is given versus a single parameter, the Fresnel number (N1). Predictions obtained by Maekawas curve deviate largely from experimental data, and from predictions obtained by analytical solutions, when the receiver is either close to the barrier or at the boundary separating the illuminated from the shadow zone. It is shown that if a second Fresnel number (N2) is appropriately defined, the IL obtained by the existing analytical solutions can be expressed versus N1 and N2 for several types of incident radiation (plane, cylindrical, and spherical). Accordingly, the single curve in Maekawas chart can be replaced by a family of curves. Each curve corresponds to a different N2 and provides the IL versus N1 . The Kurze-Anderson formula (a mathematical expression of Maekawas curve) is also modified to describe this set of curves. Besides providing increased accuracy in the areas where Maekawas curve does not, the graph proposed here addresses the more general problem of combining the simplicity of empirical models like Maekawas with the accuracy of sophisticated mathematical models.

Numerical investigation of nonlinear propagation distortion effects in helicopter rotor noisea)

The effect of nonlinear propagation distortion on helicopter rotor noise is presented based on measured data for low-speed descent and numerical calculations that predict the noise level away from the helicopter with and without nonlinear effects. It is shown that for some frequency bands the difference between linear and nonlinear calculations can be as high as 7 dB. Blade vortex interaction (BVI) noise, the dominant noise contributor during descent, is mainly examined. It is shown that advancing side BVI noise is affected by nonlinear distortion, while retreating side BVI noise is not. Based on signal characteristics at source, two quantities are derived. The first quantity (termed polarity) is based on the pressure gradient of the source signal and can be used to determine whether a BVI signal will evolve as an advancing or a retreating side signal. The second quantity (termed weighted rise time) is a measure of the impulsiveness of the BVI signal and can be used to determine at which frequency nonlinear effects start to appear. Finally, polarity and weighted rise time are shown to be applicable in cases of BVI noise generated from different blade tips, as well as in cases of non-BVI noise.

Jagged Edge Noise Barriers

A novel design of traffic noise barriers is presented: barriers that have a jagged instead of the conventional straight top edge. Experimental, numerical, and analytical investigations show that noise barrier performance can be improved by making the top edge jagged. In many, but not all, cases the jagged edge improves insertion loss, by up to 6 dB. The most promising theoretical approach is to model the edge as a directive line source. Besides yielding predictions that agree favourably with measurements, the line source model reveals that the diffracted field behind a jagged edge barrier depends strongly on the receiver location, the portion of the edge on the most direct path between source and receiver, and the inclination of the straight barrier edge segments. Further, because the model is easy to apply, it is a promising and powerful tool for design of optimum edge profiles.

Jagged‐edge noise barriers

Experimental, numerical, and analytical investigations have shown that noise barrier performance can be improved by making the top edge randomly jagged. The incident noise is a spherical N wave (produced by a spark in our model experiments). See Ho et al. [J. Acoust. Soc. Am. 101, 2669–2676 (1997)], and oral papers by (i) Menounou et al., (ii) Ohm et al., and (iii) Rosenberg et al., all in J. Acoust. Soc. Am. 101, 3075(A) (1997). In many, but not all, cases the jagged edge improves insertion loss by up to 5 dB. The most promising theoretical approach is to model the edge as a directive, crooked line source [paper (i) above]. Besides yielding predictions that agree favorably with measurements [paper (iii) above], the line source model helps in understanding the following results: (1) the jagged edge smears out the diffracted signal and makes the tail ragged, (2) insertion loss varies significantly with receiver position, and (3) the portion of the edge on the most direct path between source and receiver pl...

A generalized statistical Burgers equation to predict the evolution of the power spectral density of high-intensity noise in atmosphere

The present work is a theoretical/numerical investigation of the combined effect of nonlinearity, geometrical spreading, and atmospheric absorption on the evolution of the power spectral density of a noise field, when only the power spectral density is known at source, not the signal itself. This is often the case in aircraft noise measurements. The method presented here is based on and extends previous work [P. Menounou and D. T. Blackstock, J. Acoust. Soc. Am. 115, 567-580 (2004)], where a recursion equation [statistical Burgers equation (SBE)] describing the evolution of the joint moments of the noise source was derived. The SBE is restricted to plane waves, thermoviscous fluids, and short propagation distances (preshock region). In the present work, the SBE is extended to include the effects of geometrical spreading and arbitrary absorption, in order to be applicable to propagation of high-intensity noise through atmosphere. A new equation is derived and termed generalized SBE, and a method for its numerical implementation is presented. Results are in good agreement with time domain calculations for propagation in atmosphere of (i) sinusoidal signals (benchmark case) and (ii) Gaussian processes with known power spectral densities at source.

Analytical model for predicting edge diffraction in the time domain

A time domain model for predicting diffraction around half planes is presented. The model renders the directive line source model [Menounou, Busch-Vishniac, and Blackstock, J. Acoust. Soc. Am. 107, 2973-2986 (2000)] valid for times long after the diffracted signal arrival and for receivers close to the shadow boundaries, where it was not valid before. The presented model unifies diffraction by plane, cylindrically and spherically spreading incident signals (being exact for plane and approximate for cylindrical/spherical) and models diffraction as radiation from a directional line source. The terms describing the directivity and the line-source radiation are appropriately modified to handle diffraction by wedges and finite-length edges, respectively. The investigation of the derived formulation leads to (i) definition of universal parameters and quantities for the study of time diffraction, (ii) derivation of a generator curve that embodies the diffracted signals at any source-receiver configuration, and (iii) derivation of similarity conditions that determine how fast/slow diffraction evolves depending on the receiver location and that provide considerable computational benefit compared to direct computations. Furthermore, three time stages in every diffracted signal are identified, which allows a priori estimation of the diffracted signal characteristics based on the incident signal duration. Finally, the model is successfully applied to sonic boom diffraction on buildings.

Diffraction by jagged edge noise barriers

Experimental data have shown that the noise barrier’s performance can be improved by introducing jaggedness into the top edge of the barrier. In the present work a combined experimental/numerical investigation was performed. The numerical investigation employs the Directive Line Source Model [Menounou et al., J. Acoust. Soc. Am. 107, 103–111 (2000)] and reveals the basic global characteristics of a jagged profile that increases the shielding effect over a straight edge barrier having the same average height. For a jagged edge profile consisting of finite‐length segments inclined with respect to a straight top edge it was found that its performance depends on the inclination angle of the finite‐length segments with respect to the horizontal, the directivity of the diffracted field, and the length of the inclined segments with respect to the spatial duration of the incident sound signal. It was also found that jagged profiles offering an increased shielding effect for certain receiver locations are differen...

Directivity of the diffracted field around a half‐plane

The directivity of the diffracted field around a half‐plane barrier is investigated. Experiments were carried out in air using a spark source generating N‐shaped pulses, a capacitor microphone, and a rigid aluminum plate with: (i) straight top edge (reference case), (ii) jagged top edge, and (iii) straight edge covered with sound absorptive material. Measurements were taken around the plate by varying the angular position of the microphone while keeping its radial distance from the barrier edge constant. The following were observed: (i) Straight edge: The diffracted pulse changes polarity as it passes across the two shadow boundaries and the continuation of the barrier in the half‐space above it. (ii) Jagged edge: Although jaggedness in the top edge of the barrier drastically changes the shape of the diffracted pulse, the directivity pattern remains roughly the same. (iii) Sound absorptive edge: Although the shape of the diffracted pulse remains the same as in the reference case, the directivity patterns ...