THE ENERGY ASPECT OF THE RECIPROCAL INTERACTIONS OF PAIRS OF TWO DIFFERENT VIBRATION MODES OF A CLAMPED ANNULAR PLATE

The standardized mutual active and reactive sound power of a clamped plate, representing the energy aspect of the reciprocal interactions of two different in vacuo modes, has been computed. It was assumed that the vibrations are axisymmetric, elastic and time harmonic, the plate's transverse deflection is small as compared with the plate's size, and that the vibration velocity is small as compared with the acoustic wavenumber generated. The Kirchhoff-Love theory of a perfectly elastic plate was used. The integral formulae for the mutual sound power were transformed into their Hankel representations which made possible their subsequent computation. A closed path integral was used to express the integral in its Hankel representation to compute the mutual active sound power. The asymptotic stationary phase method was used to compute the two magnitudes, i.e., the mutual active and reactive sound power. The results obtained are the asymptotic formulae valid for the acoustically fast waves. The oscillating as well as the non-oscillating terms have been identified in the formulae to make possible their further separate analysis. The availability of the asymptotic formulae makes possible some fast numerical computations of the mutual sound power. Moreover, the formulae presented herein, together with those for the individual modes known from the literature, make a complete basis for further computations of the total sound power of the plate's damped and forced vibrations in fluid.     

Transient masking and the temporal course of simultaneous tone-on-tone masking

Previous studies have shown that threshold for a signal in tone-on-tone simultaneous masking is sometimes lower when the masker is continuous than when it is gated. Threshold may also decline as signal onset is delayed relative to the onset of a longer duration masker, though it may increase again near masker offset. In the present study, the level of a 1250-Hz sinusoidal masker was found which would just mask a 20-ms, 1000-Hz sinusoid presented at 10-dB sensation level (SL). Masker duration was 20 or 400 ms; in the latter case, the signal was presented in one of three temporal positions within the masker. The level of the 1250-Hz masker necessary to mask the signal was reduced, sometimes by as much as 20-25 dB, by a 20-ms, 500-Hz sinusoid (transient masker) presented at the times when the signal might occur, but at a level 30 dB below that at which it would mask the 10-dB SL signal. This suggests that, in the earlier studies, at least some of the elevation in threshold in the presence of a short-duration masker or at the beginning (or end) of a longer duration masker may have been due to the transient responses to the masker affecting detection of the signal, but not necessarily masking the signal in terms of excitation in the signal "channel."     

Binaural modulation masking

Modulation thresholds were measured in three subjects for a sinusoidally amplitude-modulated (SAM) wideband noise (the signal) in the presence of a second amplitude-modulated wideband noise (the masker). In monaural conditions (Mm-Sm) masker and signal were presented to only one ear; in binaural conditions (M0-S pi) the masker was presented diotically while the phase of modulation of the SAM noise signal was inverted in one ear relative to the other. In experiment 1 masker modulation frequency (fm) was fixed at 16 Hz, and signal modulation frequency (fs) was varied from 2-512 Hz. For monaural presentation, masking generally decreased as fs diverged from fm, although there was a secondary increase in masking for very low signal modulation frequencies, as reported previously [Bacon and Grantham, J. Acoust. Soc. Am. 85, 2575-2580 (1989)]. The binaural masking patterns did not show this low-frequency upturn: binaural thresholds continued to improve as fs decreased from 16 to 2 Hz. Thus, comparing masked monaural and masked binaural thresholds, there was an average binaural advantage, or masking-level difference (MLD) of 9.4 dB at fs = 2 Hz and 5.3 dB at fs = 4 Hz. In addition, there were positive MLDs for the on-frequency condition (fm = fs = 16 Hz: average MLD = 4.4 dB) and for the highest signal frequency tested (fs = 512 Hz: average MLD = 7.3 dB). In experiment 2 the signal was a SAM noise (fs = 16 Hz), and the masker was a wideband noise, amplitude-modulated by a narrow band of noise centered at fs. There was no effect on monaural or binaural thresholds as masker modulator bandwidth was varied from 4 to 20 Hz (the average MLD remained constant at 8.0 dB), which suggests that the observed "tuning" for modulation may be based on temporal pattern discrimination and not on a critical-band-like filtering mechanism. In a final condition the masker modulator was a 10-Hz-wide band of noise centered at the 64-Hz signal modulation frequency. The average MLD in this case was 7.4 dB. The results are discussed in terms of various binaural capacities that probably play a role in binaural release from modulation masking, including detection of varying interaural intensity differences (IIDs) and discrimination of interaural correlation.     

Gårding's Theory of Hyperbolic Polynomials

This paper presents a simple, self‐contained account of Gårding's theory of hyperbolic polynomials, together with a recent convexity result of Bauschke‐Güler‐Lewis‐Sendov and an inequality of Gurvits. This account begins by establishing some new results. The first concerns the existence of a pointwise arrangement of the eigenvalues so that they become global real analytic functions. The second asserts that the associated “branches” are independent of the choice of hyperbolic direction. © 2013 Wiley Periodicals, Inc.     

Thermal Characterizations of Inorganic and Organometallic Polymers

This review emphasizes the breadth of metallic and metallic-like polymers evaluated as to thermal properties. Techniques usefully applied to particular systems are noted with the aim of suggesting their application to other systems.     

Low-lying energy levels of the FeH molecule

Multireference configuration interaction (MRCI) and complete active space second-order perturbation theory (CASPT2) calculations are performed on Fe₂ and Fe^? ₂. Although it is not possible to definitively identify the ground states of Fe₂ and Fe^? ₂, the calculations suggest that the ground state of Fe^? ₂ in ⁸Σ^? _u derived from 3d¹³4σ² _g4σ² _u and that the states observed in photodetachment are the ⁹Σ^? _g and ⁷Σ^? _g states with a 3d¹³4σ² _g4σ¹ _u occupation, but that the ground state of Fe₂ is ⁷Δ_u(3d¹⁴4σ² _g) and is not observed in the photo-detachment spectra.