We investigate the effects of the δ 2 transform on the partial sums of Fourier series for functions with a finite number of jumps, which in general, converge slowly. Although the δ 2 process is known to accelerate convergence for many sequences, we prove that in this case, the transformed series will usually fail to converge to the original function.

A model for rapid computation of acoustic fields in three-dimensional, range-dependent, ocean environments [Kuperman et al., J. Acoust. Soc. Am. 88 (1990)] has been implemented on the Connection Machine and it has been extended to incorporate bottom reverberation. Bottom reverberation is treated by means of a Kirchhoff approximation to the Helmholtz-Kirchhoff integral expression for the exact Green's function using the approximate Green's function computed by the adiabatic normal-mode model as a starting point. This entails computing the integral over the bottom of the entire basin. A gridded acoustic environment is used that is mapped onto the Connection Machine's processor hypercube. This is crucial in allowing the treatment of the bottom interaction in a manner fully consistent with the wave nature of the problem without having to resort to the ad hoc introduction of plane-wave scattering amplitudes. Numerical results are shown. [Work supported by ONR, Code 1125OA.]

The Modified Rhyme Test (MRT) was processed through a room (volume 165 m3, reverberation time T= 0.4, 0.8, and 1.2 s). The tests were recorded for binaural and monaural earphone listening with a manekin Kemar and equalization amplifiers to compensate for the ear canal effect. Six groups of normally hearing subjects, 10 subjects each, had mean ages of 10, 27, 42, 54, 64, and 72 years and average Hearing Threshold Levels (HTLs) (for 0.5, 1, and 2 kHz) of 4, 6, 10, 14, 18, and 18 dB, respectively. The individual scores for MRT without reverberation were between 90% and 100%. The mean group scores for the 27-year-old group were the same for unreverberated speech and 0.4-s condition but declined for 0.8- and 1.2-s conditions. All other groups performed poorer than the young adults, e.g., the scores of the 72 year olds and the children were 16% and 8% lower, respectively. In all comparisons, the binaural scores were better than monaural ones by an average of 5%. There was a tendency for greater binaural advantages for older subjects. [Work supported by NIH.]

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