Volume 37, Issue 3, March 1965

New Method of Measuring Reverberation Time
View Description Hide DescriptionA new method of measuring reverberation time is described. The method uses tone bursts (or filtered pistol shots) to excite the enclosure. A simple integral over the tone‐burst response of the enclosure yields, in a single measurement, the ensemble average of the decay curves that would be obtained with bandpass‐filtered noise as an excitation signal. The smooth decay curves resulting from the new method improve the accuracy of reverberation‐time measurements and facilitate the detection of nonexponential decays.

Computed Frequency and Angular Distribution of the Normal Modes of Vibration in Rectangular Rooms
View Description Hide DescriptionThis paper describes the mathematical model used for computing both the frequency and angular distribution of the normal modes in rectangular rooms. The criteria adopted were computed for each half‐octave band over the first 4 octaves of normalized frequency for rooms with dimension ratios ranging from to 1:1. Considerable variation in the frequency‐spacing criterion exists not only for changes in room dimensions but also from one half‐octave band to the next. No clearly defined optimum room dimension, as predicted by Bolt, emerges from this study. The angular‐distribution index is more regularly behaved with rather definite stratification apparent as a function of the room height/length ratio, when the height direction is taken as the angular reference. When both the frequency and angular criteria are combined, only a few small regions of dimension ratios appear to be good. From these regions, p = 0.69, q = 0.43; p = 0.83, q = 0.65; p = 0.82, q = 0.72, together with p = 1/2^{1/3}, q = 1/4^{1/3}, appear to be among the best. For rooms having satisfactory mode distribution, an approximate formula has been developed for determining the lowest midband frequency for which a room may be used for measurements of continuous spectrum sounds. The formula turns out to be a constant divided by the cube root of the volume, where the constant is a function of the measuring bandwidth and the number of normal modes required therein. For 20, 12, and 9 modes in 1‐, ‐, or ‐oct bands, the constants are 1150, 1280, and 1355 cps, respectively.

Interference Patterns in Reverberant Sound Fields. II
View Description Hide DescriptionContour charts are given of the sound fields near one, two, or three reflecting surfaces at fight angles, for random sound incidence. The charts show contours of the mean‐squared pressure in decibels as a function of position in the region within two wavelengths of the boundary surfaces. The boundary conditions at the reflecting planes are pressure‐reflecting (normal velocity component equal to zero) or pressure‐release (pres‐ sure equal to zero). By reciprocity, the charts also give the relative radiation resistance of a point source as a function of position near such reflectors. The formulas used are tabulated; they extend and in some places correct formulas given in an earlier paper [J. Acoust. Soc. Am. 27, 247–258 (1955)]. The features of the sound fields near the reflectors are discussed, and some applications to acoustical measurements in reverberant sound fields are considered.

Some Experimental Observations on the dc Resting Potentials in the Guinea‐Pig Cochlea
View Description Hide DescriptionThe dc gradient across the reticular lamina, which can be as large as 185 mV, represents the algebraic difference between the endocochlear potential (EP) and the negative resting potential found within the organ of Corti. During asphyxia, the decline in CM paralleled closely the decline in this dc gradient. These data suggest strongly that CM represents a modulation of both dc resting potentials. The negative resting potential was examined further. Like EP, it is most probably extracellular, since it can be recorded with glass pipettes having a tip diameter of 25 μ. It decreases as a linear function of log K^{+} concentration in scala tympani, and it appears to be much more resistant than EP to cochlear temperature reduction.

Feedback and Noise‐Signal Detection at Three Performance Levels
View Description Hide DescriptionThe effect of the presence or absence of feedback, or immediate positive reinforcement, was studied at 3 performance levels: 88%, 75%, and 62% correct. The BUDTIF (Block Lip and Down, Two‐Interval—Forced‐choice) experimental procedure was utilized. Signal‐to‐noise ratios were varied in a 104‐trial run (about 7 min) so as to maintain the desired performance level. The noise was set to 35 dB SL. One group of naive subjects was used; each subject was presented one of the 6 conditions of performance level and feedback for 5 consecutive runs. Another group of experienced subjects was presented with all 6 conditions in each of six 1‐h sessions. Threshold signal‐to‐noise ratios, intrarun variability of levels utilized, the time per run, and interrun variability were determined. No statistically significant and systematic effect of feedback was found.

Auditory Masking in the Rat
View Description Hide DescriptionMasked thresholds were measured with an operant tracking method at 4 frequencies between 1000 and 8000 cps and at 3–5 levels of wide‐band noise. As in humans and cats, masked thresholds in the rat increased linearly with noise level. Critical ratios were calculated from the masked thresholds and found to be 10 or 11 dB greater than those in man and 5 to 6 dB greater than those in cats. Greenwood's function, relating critical bandwidths to position on the basilar membrane, was shown to fit reasonably well the data of this experiment. The constant relation shown by Fletcher between critical ratios and frequency DL's, previously found to apply to man and to cats, appears to apply to rats also.

Hearing‐Loss Trend Curves and the Damage‐Risk Criterion in Diesel‐Engineroom Personnel
View Description Hide DescriptionSeveral hundred young men were given careful audiometry before beginning duty in noise of 105–110 dB SPL at one or more of the octaves 300–600, 600–1200, 1200–2400 cps. These men were then given the same audiometric examination intervals up to five years. Less than 15% of ears had permanent threshold shifts (PTS) of more than 20 dB at any frequency. Trend curves extrapolated over log time predict a median PTS of 8 dB at 4 kc/sec for 10 years' exposure. The PTS actually found was thus 20 dB less than predicted by the ASA Z‐24 Committee report; the 4‐kc/sec TTS_{2} for an 8‐h exposure to this noise was over 60 dB; use of the 4‐kc/sec TTS_{2} index would thus vastly overpredict both the actual PTS of 8 dB and the Z‐24 Committee prediction of 22 dB. Ear defenders as actually worn by this population reduce median PTS by no more than 5 dB. It is concluded that a damage‐risk criterion of 100 dB SPL at any of the relevant octaves would be conservative, protecting at least 850/0 of young healthy ears from PTS of over 20 dB at any frequency.

Sound‐Power Production in Wind Instruments
View Description Hide DescriptionThis paper presents data for output sound powerP _{O} of wind instruments relation to input power P _{I} supplied by the player. P _{I} was calculated as pV̇, where p equals mouth pressure and V̇ air flow rate through the instrument. P _{O} was calculated from sound‐pressure level and measurements of reverberation time in a live room of known volume. A part of the data was obtained in a room of unknown characteristics; from 15 comparable measurements on 8 different instruments in both the live and the unknown room, data were obtained that allowed calculation of P _{O} also from other experiments in the unknown room. Measurements were made on single notes, played both pp and ff, on each instrument; one low and one high note on the scale of each instrument were chosen. The ratio P _{O}/P _{I}, representing the mechanical efficiency of wind instruments as sources of sound power, varies from less than 0.001% to about 2%. It appears to increase with increasing P _{I} and, in some instruments, with frequency. The consistent results obtained for 3 different flutes played by one performer suggest that the variability noted in the other data at least partially reflects individual differences in mechanical efficiency.

Thermal Relaxation in Oxygen with , HDO, and Vapors as Impurities
View Description Hide DescriptionUsing the 100% relative‐humidity technique for controlling the mole function of water vapor, the Napier (relaxation) frequency of oxygen has been measured as a function of the mole fraction of various water vapors, consisting of pure , pure , and three mixtures thereof. Pure gives, as is well known, a quadratic in H, the mole fraction; pure gives a linear relation down to 0.7×10^{−3}. The mixtures show a linear relation above 1.5×10^{−3} and a curvilinear approach to zero below that. Calculation indicates that the heterogeneous molecule HDO is far more effective as a thermal equilibrator for oxygen than either of its homogeneous parents. Quantitatively, with (f/p)_{ m } in cps per atm and h in mole fraction ×10^{3}, the results are:
100% : ;
50% : ;
80% : ;
92% : (above h = 1.3);
92% : (below h = 1.3);
99.8% : .

Control of the Acoustic Scattering Characteristics of a Rigid Sphere by Surface Loading
View Description Hide DescriptionThe problem of an acoustic wave incident on a rigid sphere “loaded” in a narrow azimuthal region is considered. The solution appears as the superposition of the field scattered by the unloaded sphere and that radiated by an active slot coincident with the load, with the radiation strength of the slot related to the loading characteristics in the combined problem. By varying the loading impedance, wide degree of control over the scattering behavior of the sphere can be achieved even when only “passive” loads are permitted. Numerical results are presented.

Acoustic‐Ray Equations for a Moving, Inhomogeneous Medium
View Description Hide DescriptionAn ordinary vector differential equation is derived for the acoustic‐ray paths in a moving, inhomogeneous medium in which the velocity and index of refraction can be general functions of position. This equation is used to obtain the curvature of the rays for an atmosphere with a constant wind and with a speed of sound that is an arbitrary function of the height. The equations of the rays are obtained as solutions in terms of quadratures, which are then evaluated in closed form for two special cases: an atmosphere with a constant speed‐of‐sound gradient and one with a constant temperature gradient.

Frequency Equations for the Normal Modes of Vibration for an Elliptical Ring, Including Transverse Shear and Rotary Inertia
View Description Hide DescriptionThe research work of Mindlin, Reissner, and Uflyand on plates is extended to the actual finding of the frequency equations for the normal modes of vibrations of an elliptical ring. Product solutions are assumed for the partial differential equations of motion and it is found that infinite series of product solutions satisfies the boundary conditions; the resulting frequency equation for each boundary condition appears as an infinite determinant, equated to zero, the elements of which are infinite series of terms involving Mathieu functions whose characteristic numbers are functions of the frequency. An algorithm is given showing how to calculate the roots of the infinite determinant that gives the normal modes of vibration. The present theory is more valid for higher modes of vibrations than the classical Lagrange theory of plates since it includes coupling between flexural and shear motions, and the numerical results, if carried out on high‐speed machines, should be valid for these higher modes.

Phase Distortion of a Pulse Caused by Bottom Reflection
View Description Hide DescriptionThe phase distortion of a plane‐wave pulse owing to bottom reflection at incident angles more grazing than the critical angle is considered. Two general methods of investigation, using the time and frequency domains, are given; they employ, respectively, the Hilbert transform of the incident pulse and the complex envelope signal. Applications to two typical SONAR pulses—a carrier frequency amplitude‐modulated by a rectangular pulse and a Gaussian pulse—are given, along with graphs of the results. It is concluded that negligible distortion occurs, there being only a phase shift of the carrier, when the Q of the waveform is moderately larger than unity, the exact value depending on the smoothness of the transmitted pulse.

Rectified Diffusion during Nonlinear Pulsations of Cavitation Bubbles
View Description Hide DescriptionA gas‐filled bubble in a liquid will generally dissolve because of diffusion of gas out of the bubble into the surrounding liquid. However, when set into motion by an acoustic field, a bubble may grow by a process called rectified diffusion. This process can counteract the effect of diffusion for values of the acoustic‐pressure amplitude greater than some threshold value. This threshold has been determined by a theory that uses computed radius‐time curves for bubbles pulsating nonlinearly rather than assumed infinitestimal, sinusoidal motions. For radius‐time curves calculated by a digital computer, this threshold has been computed for a sequence of values of gas concentration, bubble radius, and acoustic frequency.

Measurements of the Resonant Frequency of a Bubble near a Rigid Boundary
View Description Hide DescriptionThe resonant frequency of an air bubble in water near a plane rigid boundary was measured by varying the frequency of a sound source immersed in the water. The bubble was observed through a microscope and judged to be resonant when standing waves just appeared on its surface. The values of resonant frequency measured in this way, for bubbles having a radius in the range 1/10–3 cm (frequency range 100–3000 cps), were found to be in close agreement with a theory due to Strasberg. Another set of measurements over the same frequency range, for a bubble trapped in a hole that was drilled in the rigid surface, was also in close agreement with theoretical predictions. Some additional observations were made at higher amplitudes, where it was found that the presence of the hole affected the motion of the bubble in some ways. In the absence of a hole, a long time‐scale oscillation of the bubble shape was observed.

Parametrically Excited Surface Waves
View Description Hide DescriptionExperimental results are given on waves established at the upper surface of liquid in a rectangular Plexiglas vessel executing uniform vertical oscillation, with frequencies primarily in the range 50–500 cps. Comparison is made with theory originally given by Benjamin and Ursell, extended by Sorokin and Eisenmenger. Observed wave frequencies (one‐half the excitation frequency) and wavelengths are in reasonable agreement with this theory, but observed values of the critical onset amplitude ξ_{c} are much greater than expected. Considerable, though insufficient, improvement results from modifying the theory so that acoustic boundary layers at the container walls are taken into account. Using this modified theory, the ratio of observed to predicted ξ_{c} is as much as 14 at low frequency, but decreases to about 2 at the upper frequency limit. It is suggested that the discrepancy may arise, at least in part, from time‐dependent solid‐liquid surface energy, the time‐dependence resulting from oscillation of the meniscus at vessel walls.

Surface and Volume Sound from Boundary Layers
View Description Hide DescriptionIt is made plausible for turbulent boundary layers that surface, dipole sound is in general very much less than volume, quadrupole sound. This is so for two reasons. Firstly, the relative volume sound is increased by several orders of magnitude because of shear‐flow enhancement within the boundary layer. Secondly, through the use of an image argument similar to that used in the discussion of flat layers, it is indicated that the dipole sound is reduced by a factor of (L/R)^{2}, where L is the boundary layer thickness and R is the surface radius of curvature. A discussion of irregular, surface bumps shows that such imperfections may be the source of significantly large dipole sound. A calculation is given of low‐Mach‐number surface and volume sound from a rotating cylinder.

Comparison of Theoretical and Experimental Values of Spatial Correlation
View Description Hide DescriptionExperimental measurements of spatial correlation were made using the top 12 elements of a 40‐element vertical array. The hydrophone outputs were passed through filters in the 200‐ to 400‐, 400‐ to 600‐, 600‐ to 800‐, and 800‐ to 1000‐cps bands. Selected pairs of hydrophones were crosscorrelated. The experimental values of spatial correlation were compared with the theoretical values of spatial correlation. A good agreement of the experimental results with the theoretical results is obtained in the higher passbands. In general, the agreement is better for higher‐frequency bands and higher sea states. The results indicate that (1) the noise is predominantly from the horizontal direction in the 200‐ to 400‐cps band, (2) the noise is predominantly from the vertical direction in the other measured bands, and (3) the sources on the surface of the ocean radiate energy similar to that of a dipole source.
 LETTERS TO THE EDITOR


Gap between Good Acoustics for Speech and for Music
View Description Hide DescriptionScientific evidence seems to indicate that the gap between good acoustical conditions for speech and for music is irreconcilable, especially for churches. This gap is especially important to church acoustics because church music demands more reverberation than any other type of music and clarity of speech is as demanding as for any other type of auditorium. It is shown herewith that the gap is not as great as was heretofore considered.
