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+ x direction enters at time / = 0 the region x > 0 in which sound speed c( x) is a random function of position, wherc this function is drawn from an ensemble with given statistical propcrties. The wave at any positive x begins with a weak shock that arrives at a time r equal to the x integral of \/c and which, for / < r can be cxpandcd in a power senes /> r. The statistics of the cocfficicnts in this power senes are studied with the assumption that the random process c(x) is homogeneous and Gaus-sian.

9:15

6PAb2. Molecular rclaxation is irtsufficient to explain the shock structure and rise tiines of sonie booms; tur bu lence is apparently important. Thomas A. Gionfriddo, Jongmin Kang, Victor W. Sparrow, and Allan D. Pierce (Grad. Próg. in Acoust. and Dept. of Mech. Eng., Penn State Univ., P. O. Box 30, State College, PA 16804)

The authors have been recently examining somc sonic-boom wave-forms that were recorded during overflights by the Air Force and that have become available to NASA and its contractors. The quality of the digitized data and the supporting meteorological data was such that one could test the applicability of molecular rclaxation theories. In the late sixties it had been supposcd that the finite rise times of sonie booms was attributable to atmospheric turbulence, but it was later pointed out that the first estimates of rise times in the absence of turbulence had nc-glected the yibrational relaxation of nitrogen molecules. Hass et aL [J. Acoust. Soc. Am. 74, 1514-1517 (1983)1 have demonstrated that molecular relaxation definitely gives the correct order of magnitude of the observed rise times. However, the Air Force data in conjunction with the recent steady-state shock profile model theory of Kang and Pierce give the first opportunity to make a detailed quantitative assessment of the molecular relaxation hypothesis. The agreement of theory with ex-periment in some cases is remarkably excellent, but in the preponder-ance of cases the rise of the shock is slower and the rise time is longer, typically by factors of the order of 2 to 3. [Work supported by NASA-LRC and by the William E. Leonhard endowment to Penn State Univ.] ness. A previously developed numerical procedurę determines the detailed pressure versus time profile during the inten/al that the leading shock nominally occurs, taking into account molecular relaxation ef-fects, and the Fourier transform is determined using the known asymp-totic behavior of the waveform profile immediately preceding and fol-lowing the shock. The proposed definition of an effective rise time recognizes that the A-weighted sound exposure of a waveform is a good descriptor of perceived loudness and that Fourier transforms of pressure waveforms with shocks with finite rise times tend to fali off as the inverse square of inereasing freąuency as one over the square of the frequency. Such considcrations lead to a definition of rise time that is inversely proportional to the square root of the A-weighted sound cx-posure of that portion of the wavcform which ineludes the shock. The basis for this definition is explained, the constant is evaluated, and ex-amples of atmospheric sonie booms are discussed. [Work supported by NASA-LRC and by the William E. Leonhard endowment to Penn State Univ. The author acknowledges the advice of A. D. Pierce.)

10:00

6PAb5. Propagation in atmospheric convective-boundary-layer turbulence. D. Keith Wilson and Dennis W. Thomson (Dept. of Meteorology, Penn State Univ., 503 Walker Bldg., University Park, PA 16802)

Turbulence in the atmospheric convective boundary layer is inho-mogeneous and anisotropic. The vertical correlation length of the sound speed field is typically proportional to height from the ground, whereas the horizontal correlation length is proportional to boundary-layer thickness. Solutions for the turbulence strength and diffraction param-eters, valid for this particular casc, are presented. The Solutions differ significantly from those for homogeneous, isotropic turbulence. An in-tercomparison is madę between the theoretical Solutions, numerical propagation simulations, and experimental data. For the numerical sim-ulations, rays were traced through wind and temperaturę fields gener-ated by a large-eddy simulation.

9**30

10:15

6PAb6. Abstract withdrawn.

6PAb3. A statistical study of the relation between weather conditions and sonie boom waveforms. Lixin Yao, Henry E. Bass, and Richard Raspet (Phys. Acoust. Res. Group, Dept. of Phys. and Astron., The Univ. of Miss., University, MS 38677)

Sonic boom data collected at Edwards Air Force Base in Oklahoma City in the 1960s have been examined to check the validity of some common assumptions concerning the role of turbulence on sonie boom waveforms. A Turner Class was assigned to each flyby based upon reported ground weather conditions. This Turner Class was then used to indicate the presence of convective or mechanical turbulence or stable stratification. The correlation between the Turner Class and the wave-form and rise time was then calculated. These results indicate that mechanical turbulence is associated with sonie booms that have morę rounded shapes and a greater rise time than common for stable conditions. [Work supported by NASA Langley Research Center.)

9:45

6PAb4. Fourier transforms and efifecttve rise times of sonie booms propagating through a relaxing atmosphere. Jongmin Kang (Noise Control Lab., Dept. of Mech. Eng., Penn Stale Univ., 157 Hammond Bldg., University Park, PA 16802)

Sharp impulsive sounds, such as sonie booms, typically have sudden pressure jumps (shocks) that are principal contributors to their per-ceived annoyance. Rise time, the ostensiblc time over which the sudden pressure rise occurs, is somewhat of an inadequate descriptor bccausc not all profiles are similar and because two profiles with the same over-pressure and rise time may seem markedly different in perceived loud-

1952

J. Acoust. Soc. Am., Voł. 89, No. 4, Pt 2, April 1991

121 st Meeting: Acoustical Sodę ty of America

1952