Volume 27, Issue 2, March 1955

Noise of Centrifugal Fans
View Description Hide DescriptionExtensions of earlier studies [J. Acoust. Soc. Am. 26, No. 2(1953)] on ventilation system noise are reported. It is shown here that in properly engineered ventilation systems the over‐all sound power level in decibelsre 10^{13}a watt is related to the horsepower rating of the fan motor by the formula: . The octave frequency band spectrum slopes off with increasing frequency at the rate of 5 decibels per octave. The level in the first band is one decibel below the over‐all level. Measured data on fourteen fans in actual installations yield a spread of about ±4 db around these relations.

An Explosive Noise Source
View Description Hide DescriptionA 10‐gauge blank shotgun shell, exploded in a small cannon, has been used as an impulse source in performing a variety of acoustical measurements. The source has a peak power of the order of 10 000 watts with good reproducibility. The frequency spectrum simulates that of a typical turbojet engine. Instrumentation has been developed to permit simple and rapid analyses of measurements made with this source. Typical applications are described, and results obtained with the impulse source are compared to results obtained with continuous sources.

An Analog Electronic Correlator for Acoustic Measurements
View Description Hide DescriptionA study has been made of the applicability of correlation techniques to the field of acoustic measurements. The development of an analog electronic correlator for this study is reported here while the application of the correlation technique to some acoustic measurements is reported in a companion paper.
The analog correlator is divided into the following four main components and each one is discussed in detail: (1) variable time delay; (2) quarter‐squaring multiplier; (3) continuous and stepping integrators; (4) system for scanning and plotting the crosscorrelation function on both linear and logarithmic scales.
The correlator operates over an input frequency range of 100 cps to 10 kcps, a range of relative time delay τ from −15 to 190 milliseconds and RC integration times of 0.5 to 16 seconds. A dynamic range in the crosscorrelation function of approximately 50 db is achieved with ±1 db accuracy.
Special attention has been given to the errors in the crosscorrelation function resulting from finite integration time and scanning of the correlation function. A significant increase in permissible scanning speed for a given signal‐to‐noise ratio has been shown to result from “matching” the equivalent integrator pass band to that of the spectrum common to the two signals applied to the correlator. Relations have been derived between scanning speed, signal‐to‐noise ratio, and input signal band width for integration performed by either a low‐pass filter or a "matched" filter.

The Application of Correlation Techniques to Some Acoustic Measurements
View Description Hide DescriptionThis paper discusses the application of an analog correlator which computes the crosscorrelation function between two sound pressures to such measurement problems as the localization of noisesources, the determination of transmission loss, and the reduction of microphonewind noise.
The crosscorrelation function φ_{21} (r) between two nonperiodic signals will have a peak in amplitude if a component of each signal originates from a common source. The value of time delay τ for which this peak occurs equals the difference in time required for the individual components to propagate from the common source to the two points under study. An analog electronic correlator described in a companion paper has been constructed which, by employing this property of the crosscorrelation function, can separate the acoustic signal at a given point into components according to: (1) their points of origin (assuming independent sources), (2) the transit time from source to the point in question, and (3) frequency.
Preliminary experimental results show that correlation provides a practical method for determining the amount of sound contributed to the field at a given point by each of several sources. The correlator, by separating the signal transmitted directly through the structure from the flanking signal on the basis of arrival time, is also a useful tool for measuring the transmission loss of walls.

Interference Patterns in Reverberant Sound Fields
View Description Hide DescriptionIn a reverberant sound field, where at all points equal mean energy flows in all directions, it is shown that the sound energy is distributed into interference patterns the reflecting boundaries. Thus the mean energy density is not uniform at all points in the field. For a perfectly reflecting plane surface that is large compared with the wavelength, the interference pattern can be expressed as a mean squared sound pressure varying as where x is the distance from the surface and k is the wave number. Corresponding expressions are derived for the mean squared particle velocity and the mean energy density. The energy level at the surface is found to be 2.2 db higher than at points further away where the interference patterns are negligible. Similar expressions are derived for the interference patterns formed by two and three reflectors at right angles, as at the edges and corners of a room. The largest departure from uniformity occurs in a corner where the mean squared pressure is 9 db higher than at remote points. The effects of such interference patterns on transmission loss and reverberation roommeasurements are discussed briefly. The patterns are not much affected by the frequency band widths habitually used in room acoustics. Experimental confirmation of the theory is given.

Response of an Elastic Plate to Localized Driving Forces
View Description Hide DescriptionThe vibration of an infinite elastic plate when driven by a localized driving force is studied theoretically. The dilation and shear potentials are expressed as Fourier integrals, the boundary conditions are applied, and the integrals evaluated by the calculus of residues. It is found that the motion of the plate may be represented by a discrete sum of nonorthogonal eigenmodes. These modes represent two types of waves, propagated and attenuated. The former are obtained from previous work on coincidence transmission. The latter are calculated by a graphical method, and presented in such a manner that they tie in continuously with the propagated modes. Certain unresolved features of the problem are discussed. One previous application of the theoretical results is disclosed.

Fundamental Frequencies of Clamped Triangular Plates
View Description Hide DescriptionApproximate solutions are given for the fundamental frequencies of flexural vibration of flat triangular plates with all edges clamped. The plate equation is written in skew coordinates and the method of collocation is used to obtain the approximate solutions. Results are presented in simple graphical form so that one may determine rapidly a desired fundamental frequency.

An Acoustic Intensity Meter
View Description Hide DescriptionA device is described for measuring the intensity of an acoustic wave at a point. The instrument employs a crystal microphone as a pressure transducer, directional hot‐wire anemometer as a velocitytransducer and an electronic multiplier and integrator. We can directly measure the intensity for any pressure or velocitywave form without having to assume any relationship between pressure and velocity. Several types of measurements have been made to indicate the present capabilities of the instrument.

Note on the Propagation of Normal Modes in Inhomogeneous Media
View Description Hide DescriptionGiven a wave duct with continuously variable parameters extending from y=0 to y=H, the reflection coefficients for originally plane downgoing and upgoing waves are written in the form and , respectively. It is then shown that the characteristic equation governing the dispersion of undamped normal modes in the medium is , m being an integer defining the mode number. χ↓ and χ↑ are solutions of nonlinear first‐order differential equations. If the medium consists of n homogeneous layers of finite thickness, the differential equation is replaced by a recursion relation, and the characteristic equation shown above includes one additional term.

Studies on Acoustic Radiation Pressure. I. (General Considerations)
View Description Hide DescriptionThe equation derived by Kotani and King relating to the excess pressure valid to the second order in the acoustic field is examined. It is shown that the solution of the usual wave equation can be used in the case when the radiation pressure in the Langevin's sense is derived from this equation. The reason as to why not only the normal force but also the tangential force on the nonstiff surface result due to the radiation pressure defined from the viewpoint of the pressure in hydrodynamics, is clarified by considering the motion of the surface. The general expression for the radiation pressure on the rigid object which is in motion due to inertia effect, is led by introducing moving coordinates.

Studies on Acoustic Radiation Pressure. II. (Radiation Pressure on a Circular Disk)
View Description Hide DescriptionA general formula for the radiation pressure acting on a thin rigid circular disk is derived from the theory of the previous paper. Motion of the disk under action of the wave and diffraction of the wave due to the disk are taken into account. Constants which may be calculated by the use of the oblate spheroidal functions necessary in obtaining the radiation pressure are given in the table. Numerical calculation for disks of various weight with the ratio of the circumference of the disk to the wavelength of sound up to 3.5 is carried out.

Underwater Ultrasonic Scattering by a Radial Cylindrical Temperature Gradient
View Description Hide DescriptionThe scattering of a one‐megacycle underwater ultrasonic beam by a radial cylindrical temperature gradient perpendicular to the beam is studied as a function of position and gradient strength. The gradient is produced by a vertical hot wire. The presence of free convection currents makes necessary time average study of both the temperature and scattering distributions. From these studies average temperature and scattering distributions are constructed, and it is found that a possible diffractive transition region exists between temperature gradients of 14.5 and 26.5°C/cm. In addition, there is evidence that a transition from wave to ray acoustics occurs between gradients of 26.5 to 36.5°C/cm.

Ultrasonic Attenuation Studies in Biased Ceramics
View Description Hide DescriptionThe attenuation of pulsed 10‐megacycle ultrasound in bariumtitanateceramics is studied as a function of temperature and applied field. In the region of the coercive field strength attenuation maxima are observed which correlate with a rapid change of the electromechanical response. Both phenomena can be traced to domain wall movements of two different kinds. A model is proposed which identifies one kind of attenuation maximum with a stress equalization in the polarized crystal grains of a ceramic, and the other kind with the nucleation of antiparallel domains. In both cases the losses appear to be caused by an elastic hysteresis due to dislocation movement.

A Method of Transducing an Ultrasonic Shadowgraph or Image for Display on an Oscilloscope
View Description Hide DescriptionIt is found that the pattern of piezoelectric voltage on the surface of a resonant crystal corresponds to the pattern of the exciting ultrasonic field. A capacity scanning system is described whereby ultrasonic shadow‐graphs and images are reproduced for observation in a manner similar to that used in television.

Transducer Design for Ultrasonic Delay Lines
View Description Hide DescriptionThe problem of obtaining low loss ultrasonic delay lines for switching, computer, and certain radar applications is discussed. An analysis is made of structures using half‐wavelength and quarter‐wavelength bonds between the transducer and the acoustic medium to widen the pass‐band; results are listed for both quartz crystal and bariumtitanatetransducers.
For bariumtitanatetransducers (80 percent , 12 percent , 8 percent ), it is shown that a theoretical flat band width of approximately 30 percent with less than 1 db midband loss can be obtained with a bond of negligible thickness. This band width can be increased to approximately 46 percent without additional loss if a properly designed bond is used, (i.e., bond for radiating into water, for use with a fused silica delay medium). A 70 percent band width can be obtained with only 4 db loss per transducer.
Confirming experimental results are described for delay lines using quartz crystals and one‐half wavelength plastic seals or one‐quarter wavelength solder seals. For the latter, band widths of 85 percent of midband frequency have been obtained. An efficient delay line using transducers is also described.

Elastic Wave Velocities in Laminated Media
View Description Hide DescriptionThe velocities of elastic waves in a laminated medium have been determined by calculating the effective elastic parameters and the effective density. The procedure is to assume the medium to be in static equilibrium and exposed to certain stresses. The stresses are of such a nature as to generate strains similar to those which would exist during the passage of an elastic wave through the medium. From the application of Hooke's law, an effective stiffness constant for the medium is obtained. The ratio of this effective stiffness to the effective density is the square of the velocity of the elastic wave. For a medium consisting of layers of two materials with the same density but with a velocitycontrast of two (2), the velocity of compressional waves traveling parallel to the layering is 20 percent higher than the velocity of the same wave traveling perpendicular to the layers. The SH shear wave has a velocity which is 25 percent higher than the SV shear wave for the same laminated medium.

Elastic Constants of Aluminum from 20°C to 400°C
View Description Hide DescriptionThe use of the ultrasonic pulse technique as a means of determining the elastic constants of polycrystallinealuminum at high temperatures has been considered in some detail.
The and elastic constants, Debye temperature, and Young's modulus were computed from the longitudinal and transverse velocity measurements. The variations of these constants with temperature showed the predicted linear decrease expected from solid state theory.

Ultrasonic Dispersion in 1,1‐ and 1,2‐Dichloroethane Vapors
View Description Hide DescriptionThe ultrasonic resonator interferometer has been used to measure the ultrasonic velocity at 30°C in 1,1‐dichloroethane (ethylidene chloride, ) and 1,2‐dichloroethane (ethylene chloride,) vapors as a function of frequency over pressure. The ranges f/p employed are 0.8 to 100 Mc sec^{−1} atmos^{−1} in the case of ethylidene chloride and 1.0 to 100 Mc sec^{−1} atmos^{−1} in the case of ethylene chloride. The velocities have been corrected for nonideality of the two vapors. Dispersion of ultrasonic velocity occurs in both the cases and this is ascribed to the slow rate of energy exchange between translational and vibrational states. There is evidence of double relaxation in the two cases, the principal f/p ratios at 30°C being 76.5 Mc sec^{−1} atmos^{−1} for the former and 102 Mc sec^{−1} atmos^{−1} for the latter.

The Apparent Reduction of Loudness: A Repeat Experiment
View Description Hide DescriptionThe experiment of Laird, Taylor, and Wille (1932) showed that the reduction in the intensity of a sound required to produce half‐loudness is of the order of 20 db. Since this result is out of line with most other studies in this field, an attempt was made to repeat the experiment with a similar piece of apparatus (2‐A audiometer). The first attempt to copy the procedure of Laird, Taylor, and Wille gave results more like those usually obtained, namely, a required reduction for half‐loudness of the order of 10 db. A second experiment, involving the use of comparison tones placed as much as 40 db below the standard, gave results more like those of Laird, Taylor, and Wille. The method they used appears to be overly sensitive to the range and order of presentation of the comparison stimuli.