Index of content:
Volume 62, Issue 3, September 1977

Propagation of audible sound through air‐water fogs
View Description Hide DescriptionThe propagation of audible sound through air‐water fogs is studied theoretically using a generalized Burgers’ equation applicable to media exhibiting relaxational as well as classical thermoviscous absorption. The effects of vibrational and rotational relaxation of the gas molecules, and of polydisperse waterdroplet relaxation due to mass, momentum, and heat exchange with the gas are included in the formulation. Analytic expressions showing the dependence of dispersion and attenuation parameters on gas and dropletproperties and on sound frequency are derived. Agreement between theoretical predictions and available experimental measurements is good. The results clarify those conditions under which sound propagation in fogs is significantly different from propagation through humid air containing no suspended droplets.

High‐frequency acoustic scattering from submerged cylindrical shells coated with viscoelastic absorbing layers
View Description Hide DescriptionWe analyze the high‐frequency scattering of a plane‐wave incident on a submerged air‐filled cylindrical steel shell coated with a viscoelastic layer. The scatteredpressure field consists of a geometrical acoustic contribution and another part due to creeping waves. We analyze the resulting generalized reflection coefficient as a function of azimuthal angle, for two shell sizes and various viscosity levels of the coating. We also obtain the locations of roots of the 10×10 characteristic determinant in the complex ν‐plane for the two shell sizes of interest. These zeroes are compared to the zeroes of rigid and soft cylinders and to the roots of a simpler 3×3 determinant corresponding to the case of a solid sound‐absorbing cylinder of the same size. The results show that the region in the ν‐plane where many of the roots are usually concentrated for bare structures, contain no roots after the absorbing layer is bonded to the steel shell. All the above information is then used to compare the normal‐mode solution for the sonar cross section of the coated cylindrical shell found in an earlier study of ours (and extended here to higher k _{1} c values), and the corresponding expression obtained to lowest order from an application of the Watson–Sommerfeld transformation. This comparison, as exhibited in various graphs, is found to be very favorable. It verifies that the lowest‐order term in the Watson–Sommerfeld transformed solution is capable of accurately reproducing the exact scattering solution at high frequencies for the cylindrical coated target considered here.

Acoustic reflection from cylinders—nonabsorbing and absorbing
View Description Hide DescriptionThe reflection of an acoustic plane wave by an elastic cylinder of infinite length, which may absorb energy, is calculated and measured. Computations of reflection by an infinitely long elastic cylinder as a function of frequency and angle, are compared with experimental data taken using finite cylinders immersed in water. Good agreement is obtained.

Finite‐amplitude saturation of plane sound waves in air
View Description Hide DescriptionWhen the received level of a transmitted acoustic wave reaches an upper limit that cannot be exceeded regardless of how much acoustic power is radiated by the source, the wave is said to have saturated. Experiments on saturation of plane waves in air are reported in this paper. The measured quantity is the pressure amplitude p _{1} of the fundamental. To obtain a theoretical prediction that is valid close to and including saturation, we assume the decay rate of the fundamental is the sum of the sawtooth and ordinary absorption decay rates (Rudnick’s assumption). Solution of the assumed equation gives p _{1}=2p _{10} e ^{−αx }/[1+(1−e ^{−αx })/α?], where p _{10} is the source amplitude, α is the ordinary (small‐signal) attenuation coefficient, and ? (proportional to 1/p _{10}) is the shock formation distance. The saturation amplitude is found by letting p _{10}→∞. The experiments were done in a plane‐wave tube over a frequency range of 0.5 to 4 kHz at source levels up to 163 dB (r e 0.0002 μbar). Qualitatively, saturation is evident in the waveforms and the amplitude response (input–output) curves. Quantitatively, the data confirm the theoretical prediction. Dispersion, which is caused by tube‐wall boundary layer effects, causes asymmetry of the waveforms but apparently has little effect on the fundamental amplitude.

Concerning the influence of echo carrier frequencies and antenna dimensions on the performance of echosonde (acoustic‐radar) antennas
View Description Hide DescriptionA study of the influence of echo carrier frequencies and antenna dimensions on the performance of acoustic‐radar antennas is reported with features of practical interest. For a steady‐state plane‐wave propagation, appropriate expressions are given for the acoustic impedance, the homogeneous boundary conditions analogous to the electromagnetic type of problems, and the time‐averaged acoustic energy. Diffraction pattern integral equations for echosonde antennas are evaluated in closed forms using the Zernike polynomials and the generalized‐hypergeometric functions, and physical interpretations are given where appropriate. Accurate computer simulations can contribute toward: (1) Better understanding of acoustic remote sensing of atomspheric structure/properties and (2) time‐saving/avoidance of hidden problems in field work. Antenna‐pattern simulations are examined using modifications of antenna design which improve antenna‐system performance. By proper choices of echo carrier frequencies and antenna dimensions, quasiuniform phase distributions pertinent to modest phase shifts of experimental measurements (in striking contrasts with rapidly changing phases of previous results), are obtained. Severe side lobes are major detriments in acoustic remote sensing. Results presented include computer simulations of an antenna employed in probing the marine atmosphere remotely from a moving ship during a cruise in the Pacific Ocean/Caribbean Sea, and simulations of an antenna employed over dry‐land; ground‐level side lobes versus echo carrier frequencies; and 3‐dB beamwidth variations with echo carrier frequencies and with antenna dimensions. For 1–5‐kHz carrier‐frequency range, acceptable antenna dimensions are 1.22, 1.8, and 1.8 m for the illuminating‐ transmitting‐aperture diameters, and height of the absorbing cuffs, respectively. Half‐power beamwidths within 7°–13.5° are obtained in the 1–2‐kHz frequency range; and selection of antenna flare angles between 15° and 18° tends to give optimum side‐lobe attenuations. Comparisons between theory and measurements show overall good agreements. Maximum relative side‐lobe rejections of about −56.5 dB (in good accordance with measurements) in the 20° region near the ground, are obtained at 2‐kHz carrier frequency.

Modifying the sound‐speed profile to improve the accuracy of the parabolic‐equation technique
View Description Hide DescriptionThe parabolic‐equation technique has received considerable attention since its introduction to the underwater‐sound community by Tappert and Hardin three years ago. The technique relies upon removing the primary radial dependence of the acoustic field from the elliptic wave equation, and approximating the resulting equation with a parabolic (or Schroedinger) equation which may then be rapidly solved on digital computers. The parabolic approximation has been shown for layered media to result in an error in the phase velocity of the normal modes. In underwater‐sound propagation the phase‐velocity error can cause substantial shifts in the range of convergence zones. A significant reduction in this error appears achievable by a simple modification to the refractive‐index profile n (z) which transforms the (n,z) pairs of points into a new set of points (?,?). Within the accuracy of the WKB approximation, the normal modes for this new environment have the same phase velocities as the equivalent wave‐equation modes in the original environment. The z to ? mapping indicates the correspondence between field points in the old and new environments. This mapping is designed to approximately map turning point into turning point. Comparisons with normal‐mode solutions of the full elliptic wave equation are presented to illustrate the improvement in accuracy of the parabolic results under this transformation. A ray comparison is also given. Problems associated with extending the technique to a range‐dependent environment are discussed and in limited testing have been found to be minimal.

Speed of sound in deuterium oxide relative to normal water as a function of temperature and pressure
View Description Hide DescriptionThe speeds of sound of liquid deuterium oxide relative to normal water were measured at 1 atm over the temperature range of 4°–60°C and at pressures up to 1000 bars over the temperature range of 5°–50°C. Three velocimeters were used to measure the sound speeds of deuterium oxide at 1 atm relative to normal water. These three sets of 1‐atm data were fitted to a polynomial equation of temperature with a standard deviation of ±0.09 m/sec. The results of the high‐pressure measurements were fitted to an equation of the form (with a standard deviation of ±0.07 m/sec) (U _{H} _{ 2 } _{O}−U _{D} _{ 2 } _{O})−(U ^{0} _{H} _{ 2 } _{O}−U ^{0} _{D} _{ 2 } _{O} ) =AP+BP^{2}+CP^{3}+DP^{4}, where U _{H} _{ 2 } _{O} and U _{D} _{ 2 } _{O} are, respectively, the speeds of sound in normal water and deuterium oxide (superscript zero denotes 1 atm). A, B, C, and D are temperature‐dependent parameters which were determined by the least‐squares method. Although the values of U ^{0} _{D} _{ 2 } _{O} obtained in this study are on the average 0.6 m/sec lower than the data of Wilson [J. Acoust. Soc. Am. 33, 314–316 (1961)], the pressure effect on the relative sound speeds from the above equation [(U _{H} _{ 2 } _{O}−U _{D} _{ 2 } _{O}) −(U ^{0} _{H} _{ 2 } _{O}−U ^{0} _{D} _{ 2 } _{O})] agree with the work of Wilson to an average of 0.26 m/sec. One atmosphere adiabatic and isothermal compressibilities for deuterium oxide which are reliable to ±0.005×10^{−6} bar^{−1}, were calculated from the sound‐speed data. The results were compared with the data of various workers. The values of isothermal compressibility obtained in this study are systematically higher than the work of Fine and Millero [J. Chem. Phys. 63, 89–95 (1975)] (average 0.05×10^{6} bar^{−1}); however, they agree with the data of Millero and Lepple [J. Chem. Phys. 54, 946–949 (1971)] and Emmet and Millero [J. Chem. Eng. Data 20, 351–356 (1975)] to within ±0.02×10^{−6} bar^{−1}.

Sound absorption in sea water
View Description Hide DescriptionAn equation is presented for sound absorption in sea water as a function of frequency, temperature, and pressure based on laboratory data. The equation includes contributions to absorption due to boric acid,magnesium sulfate, and water. The effect of pressure on sound absorption due to magnesium sulfate and water has been treated differently than in the Schulkin and Marsh equation. At 4°C our results for absorption at frequencies from 10–400 kHz and pressures up to 500 atm are substantially lower than those calculated from the Schulkin and Marsh equation.

Sensitivity of piezoceramic tubes, with capped or shielded ends, above the omnidirectional frequency range
View Description Hide DescriptionThe NRL computer program SHIP is used to compute the diffraction constants for finite‐length cylindrical radiators and circular pistons in the end of finite‐length cylindrical baffles. Radiation impedances are calculated. The diffraction constants can be used to calculate the sensitivity of piezoceramic tube elements above the omnidirectional range.

Absorption of sound in air: High‐frequency measurements
View Description Hide DescriptionThe absorption of sound in air at frequencies from 4 to 100 kHz in 1/12 octave intervals, for temperatures from 255.4° K (0° F) to 310.9° K (100° F) in 5.5° K (10° F) intervals, and at 10% relative‐humidity increments between 0% and saturation has been measured. The values of free‐field absorption have been analyzed to determine the relaxation frequency of oxygen for each of the 92 combinations of temperature and relative humidity studied and the results are compared to an empirical expression. The relaxation frequencies of oxygen have been analyzed to determine the microscopic energy‐transfer rates.

Sound‐tube measurements of the relaxation frequency of moist nitrogen
View Description Hide DescriptionAt audible frequencies, the vibrational relaxation of nitrogen contributes significantly to the absorption of sound in still air. The accurate measurement of the humidity dependence of the relaxation frequency of nitrogen, as yet, has eluded careful measurement due to the difficulty in measuring small absorption at low frequencies. Recently, equipment has been constructed for measuringsound absorption in air as a function of humidity over the frequency range from 4 to 100 kHz. In the experiment described here, the temperature and humidity range of this equipment has been extended so that it can be used to study the relaxation absorption in nitrogen at temperatures from 311° K to 418° K. The results indicate that, over this temperature range, the frequency of maximum absorption in moist nitrogen, f _{ r,n }, can be given by f _{ r,n }/P=260×h, Hz/atm, where h is the percent mole fraction of water, and P is the pressure in atm. To the accuracy of the measurements reported here, f _{ r,n } is independent of temperature over the range of temperatures at which the measurements were made.

Ultrasonic absorption in liquid selenium
View Description Hide DescriptionThe temperature and frequency dependence of the ultrasonicabsorption coefficient in molten selenium have been studied in the range from 200° to 400° C and from 30 to 70 MHz. The data are consistent with the values in the literature for the high‐temperature range but supersede the previous results below 300° C. A theoretical model is prepared in which the monomer (rings) of the selenium represent a nonrelaxing component with the polymer chains forming a relaxing component.

Experimental assessment of the Mindlin–McNiven rod theory
View Description Hide DescriptionThe three‐mode theory due to Mindlin and McNiven, [J. Appl. Mech. 27, 145–151 (1960)] governing axisymmetric motions in a circular rod, is appraised by comparing responses predicted by it with experimental data obtained by Miklowitz and Nisewanger [J. Appl. Mech. 24, 240–244 (1957)]. The problem studied involves a semi‐infinite rod, made of 24S‐T aluminum alloy, subjected to pressure applied to the end of the rod. The two sets of responses are compared at various stations along the rod. To make the comparisons meaningful, it was necessary to recognize that the pressure applied experimentally had a finite rise time, however short; to make an estimate from the responses of what that rise time might be; and then apply this time distribution of pressure in evaluating the theoretical responses. Comparison shows that the Mindlin–McNiven theory predicts the responses at stations farther than one diameter from the end of the rod. The matching is accurate not only at the head of the impulse but at points representing large times following the first disturbance.

Vibration of tubes conveying fluids
View Description Hide DescriptionGeneral, nonlinear equations are derived for the vibration of rectilinear tubes conveying incompressible fluid. From these equations are obtained the equations for small vibrations. If values of tube frequencies and critical flow parameters are to be predicted accurately, the initial state of stress must be taken into account. A numerical example is considered.

Acoustical scale model study of the attenuation of sound by wide barriers
View Description Hide DescriptionAcoustical scale modelexperiments carried out with building‐size barriers are described. The results of experiments conducted with the barrier in a free field and on a reflecting surface are presented. The free‐field measurements are compared to several theoretical models and discrepancies between the theoretical and experimental results are discussed. Also presented is a simple expression which relates the excess attentuation obtained with the barrier situated on the ground to that of the same barrier in the free field. This expression predicts excess attenuations which agree quite closely with those actually measured in the scale modelexperiments.

Model for the relative salience of the pitch of pure tones presented dichotically
View Description Hide DescriptionThe perception of dichotic chords is characterized by two unique properties—invariance of the relative salience of the two pitch components with respect to large interaural intensity differences (’’intensity independence’’) and a tendency for the tone delivered to one ear to be relatively more salient (’’ear dominance’’) [Efron and Yund, J. Acoust. Soc. Am. 59, 889–898 (1976)]. A simple model is described which can account for these effects and the changes in the magnitude of these effects as a function of stimulus parameters. The model assumes (1) the existence of tuned frequency specific monaural filters, (2) a compressive intensity‐response function, and (3) a central combination of corresponding monaural channel responses. The model’s performance is not only consistent with all previously published experimental data but also anticipates experimental results described in the two companion papers.

Effects of signal intensity and noise on the pitch mixture of dichotic chords
View Description Hide DescriptionThe relative salience of the two pitch components (the pitch mixture) of a two‐tone dichotic chord (one tone to each ear via earphones) has been shown to be invariant with respect to the interaural intensity difference (ΔI) over a wide range of ΔI [Efron and Yund, J. Acoust. Soc. Am. 59, 889–898 (1976)]. This range of invariance of the pitch mixture was systematically studied as a function of absolute signal level and signal‐to‐noise ratio. Results indicate that a decrease in the signal‐to‐noise ratio and a decrease in the sound‐pressure level both served to decrease the range of interaural intensity differences over which the invariance occurs. However, while a decrease in both parameters decreased the range of intensity independence, there was a strong interaction between these parameters: The addition of noise eliminated the effect of sound‐pressure levels. These findings are discussed in the context of the model described in the companion paper [Yund and Efron, J. Acoust. Soc. Am. 62, XXX–XXX(1977)].

Ear dominance in dichotic chords and ear superiority in frequency discrimination
View Description Hide DescriptionFrequency‐discrimination thresholds were determined for pure tones presented either to the right or to the left ear of experienced listeners. In some conditions the stimulus was monaural, whereas in others a tone of fixed, different frequency was simultaneoulsy present in the contralateral ear. Center frequencies of 1.2, 1.7, and 3.2 kHz were investigated. Results reveal a small but reliable discrepancy between just noticeable frequency differences obtained for the right and for the left ear, both in the monaural and in the dichotic conditions. Furthermore, the direction and the degree of asymmetry with respect to the frequency resolving power of the two ears showed a correlation with the direction and the degree of ear dominance for the pitch of dichotic two‐tone complexes. [See Efron and Yund, J. Acoust. Soc. Am. 59, 889–898 (1976).] Implications of the relationship between the two types of functional asymmetry of the auditory system are discussed.

Lateralization model and the role of time‐intensity tradings in binaural masking: Can the data be explained by a time‐only hypothesis?
View Description Hide DescriptionIn an earlier paper [J. Acoust. Soc. Am. 50, 1116–1122 (1971)] I presented a lateralization model of binaural masking‐level differences (MLD’s), according to which detection under conditions which produce an MLD is based on the average value of an interaural parameter, Δ. This factor is made up of interaural time (Δt) plus interaural intensity (ΔI) weighted by a binaural trading ratio (TR). Two figures in that paper depicted application of the model to MLD’s found as a function of frequency [(Hirch and Burgeat, J. Acoust. Soc. Am. 30, 827–832 (1958)]; those figures are partially incorrect. They show the lateralization equation with a time‐intensity trading ratio of 20 μsec/dB to be the best fit, when in fact, the fit to TR=0 μsec/dB is excellent. The lateralization model with a trading ratio of 0 is very much like the vector model of Webster [J. Acoust. Soc. Am. 23, 452– 462 (1951)] and Jeffress e t a l. [J. Acoust. Soc. Am. 28, 416–426 (1956)]. It is suggested here that variability in the noise process may be significant factor, allowing binaural neurons tuned to high frequencies to recover and then respond again to interaural differences of time.

Detection threshold for a two‐tone complex
View Description Hide DescriptionThe absolute threshold for two‐component tone bursts of 500‐msec and 1‐sec duration was measured as a function of the frequency spacing between the components. The average frequency of the two components was 700 Hz. When interpreted in terms of an energy‐detector model (peripheral filter followed by squarer, integrator, and threshold detector), the measurements give an estimate of the time constant and window shape of the integrator. Our measurements on two subjects give a time constant on the order of 200 msec. A window which initially decreases more rapidly than exponentially fits the data better than an exponential window.