Volume 25, Issue 5, September 1953

Transformer Couplings for Equivalent Network Synthesis
View Description Hide DescriptionIt may be shown that regardless of the type of analogy chosen (“impedance” versus “mobility”), disconformity will be encountered in synthesizing the equivalent network of a mechano‐acoustic array. A method is described employing transformer couplings for getting around this difficulty. As a result, it becomes possible to construct equivalent circuits of mechanical arrays in a simple and straightforward manner by the method of impedance analogy. Similar benefits are achieved for the method of mobility analogy in the synthesis of equivalent circuits of acoustic arrays. Equivalent networks for certain mechano‐acoustic arrays which cannot be conventionally synthesized become feasible through this method.

Equivalent Network Representations for Solid and Mercury Delay Lines
View Description Hide DescriptionAn equivalent network representation is derived for mercury and solid delay lines. A transfer function that relates output voltage to input voltage is the quantity selected to represent the delay line, and this transfer function is derivable from a matrix equation.Mercury and solid delay lines are compared in terms of the gain band width product of the delay line. The comparison extended to include factors not present in the circuit representation. Other topics discussed are third‐time‐around signals, acoustic transformers, glued crystals, input impedance, wave propagation, and diffraction. The final selection between solid and mercury delay lines is determined by the specific application.

The Impedance of a Resistance Loaded Helmholtz Resonator
View Description Hide DescriptionThe impedance of a Helmholtz resonator damped by a thin porous layer in the form of a screen or cloth is calculated as a function of the distance between the aperture and the screen. It is shown that the input resistance of the resonator decreases very fast as the distance between the screen and aperture increases, whereas the aperture mass reactance passes through a maximum. The importance of these results with regard to design of resonators and perforated facings is discussed.

Acoustic Impedance of Rectangular Tubes
View Description Hide DescriptionAn expression for the acoustic impedance of a section of infinite parallel planes is derived. Measured values of the impedance of long narrow rectangular tubes show good agreement with this theory when an appropriate end correction is used. The theory compares favorably with impedance measurements on short rectangular tubes or slits even when the effective length of the slit is 3.7 times the geometric length.

End Corrections for a Concentric Circular Orifice in a Circular Tube
View Description Hide DescriptionThe results of an experimental investigation of the end corrections for acoustic resistance and acoustic inertance for a concentric circular opening in a partition in a circular tube are presented. The end corrections are taken to be that length which must be added to the geometrical length of the orifice when introduced into an expression for the acoustic impedance. This expression can be derived on consideration of a tube of infinite length failed with a viscous, incompressible fluid. Used in this manner, the two end corrections are found to take on the same values, these values agreeing with those derived for inertance on the basis of the mass contribution due to higher order waves in the tube, treating the orifice as a plane piston source. Graphical criteria for the onset of measurable nonlinearity are presented.

A Miniature Piezoelectric Microphone
View Description Hide DescriptionA new rochelle salt microphone has been developed for use as a secondary standard in production testing, sound level measurements, high quality transmission of sound, and similar applications. The diameter of the new microphone is half the diameter of similar units in current use. Frequency response, directional characteristics, and moisture protection have been improved without a significant loss in sensitivity.

A Miniature Microphone for Transistorized Amplifiers
View Description Hide DescriptionA new magnetic microphone has been developed for use in hearing aids and communication and similar equipment which requires a small, light, medium‐impedance microphone. The new microphone has a diameter of 1 inch and a thickness of , and it weighs 10 grams. The sensitivity is high enough to override the relatively high noise level of transistors in the frequency range most useful for voice transmission.

The Theoretical Sensitivity of Three Types of Rectangular Bimorph Transducers
View Description Hide DescriptionThe theoretical sensitivity for operation below resonance of three types of rectangular, bimorph transducer elements is derived using the results of elasticity theory. The cases treated are first, the widely used corner‐loaded square bimorph; second, the rectangular bimorph simply supported along two sides and uniformly, transversely loaded; and third, the latter loaded only over a strip in its center.

Barium Titanate Admittance‐Temperature Characteristics
View Description Hide DescriptionThere is a large amount of data in the literature describing the temperature effects on the dielectric and piezoelectric constants of bariumtitanate. This paper, however, describes the temperature effects on the admittance of bariumtitanatetransducers operating near resonance. Both “pure” and leaded ceramic mixtures are compared over the 0–20°C temperature range. Some results of calcium additives are also given. Despite extreme fluctuations of the dielectric and piezoelectric constants over this temperature range, it is possible at certain frequencies near resonance for the transducer conductance and susceptance to vary very little with temperature. Water admittance circle diagrams and power‐frequency curves—all plotted at different temperatures—are presented and analyzed from an equivalent circuit point of view. One of the significant conclusions derived from this experiment is that the radiated power of even a pure ceramic transmitting transducer, properly matched to its source at this optimum frequency, will remain maximized regardless of the temperature variation. While the bariumtitanate temperature effects were studied for given underwater transducers, the information outlined is of value to anyone encountering temperature variations in a resonant bariumtitanateceramic.

Optimum Directivity Patterns for Linear Point Arrays
View Description Hide DescriptionThe sharpest major lobe of a directivity pattern due to a linear array of equally‐spaced point elements is achieved when the elements are excited in such a manner that all minor lobes in the pattern have the same relative amplitude. Methods of producing such equal‐minor‐lobe patterns originally given in the radio literature by C. L. Dolph and by H. J. Riblet are summarized briefly in this paper. In particular, the synthesis method indicated by Riblet is described in general terms, and the effect of the element spacing is discussed in detail. Included in this discussion is the subject of super‐directivity. Results of numerical calculations based on these methods are presented as families of curves showing the relationships existing among angular width of the major lobe, relative amplitude of the equal minor lobes, directivity index, and number and spacing of the elements in the array for 5–13 odd numbers of elements. In addition, the synthesis methods are extended to compensated, or steered, arrays.

On the Measurement of Power Radiated from an Acoustic Source
View Description Hide DescriptionThis paper describes an experimental test of the theory that the total force on an absorber receiving a beam of plane waves is a measure of the acoustic power generated at the source, provided that certain conditions are satisfied. The exponential decay in acoustic intensity is accompanied by a corresponding exponential increase in the force due to the hydrodynamic flow, as has been verified experimentally. The sum of these two forces, plus a possible further force that may exist at the emitting surface due to local hydrodynamic conditions or to a “pumping effect,” should be independent of the distance from the source to the absorber. The verification of this prediction is the chief result of the investigation. From the results it can also be inferred that the “pumping effect,” if it exists at all, is probably very small in liquids.
As absorbers, slab of ρcrubber, a 90° wedge, and a cavity radiometer were used.
The reacting force on the transducer was also measured, and found, within the limits of measurement, to be equal to that on the absorber. This result indicates that acoustic power can be measured by observing this reacting force without the need of an absorbing system.

The Sound Field of a Moving Source
View Description Hide DescriptionThe sound fieldgenerated by an ellipsoidal vibrator, moving with constant velocity, is examined. The solution has the form of an infinite series. The first term of the series agrees with the solution for a point source, established by previous investigators.

The Concept of Radiation Scattering and Its Application to Reinforced Cylindrical Shells
View Description Hide DescriptionThis paper presents an approach which permits the analysis of elasticscatterers embodying complicated structural characteristics. Such problems cannot be investigated by means of the methods previously applied to the study of the scattering action of simple elastic bodies.
The scatteredwave pressure produced by elasticscatterers may be expressed as the sum of two terms, one representing “rigid body scattering,” i.e., the scattering which would exist if the scatterer were rigid and immobile, the other representing “radiation scattering,” which is associated with the sound radiated by the scatterer vibrating under the effect of the incident wave pressure. These two terms are derived here for three important cases.
The problem is now reduced to one in elasticity, specifically to the problem of solving the equations of motion of the elastic system for its forced response. The scattering pattern can then be computed. This procedure is applied to a scatterer in the form of a cylindrical shell reinforced with regularly spaced septa.

On the Vibration of Mass‐Loaded Membranes
View Description Hide DescriptionThe conventional treatment of a vibrating membrane with a small mass load, originated by Rayleigh, leads to perturbed eigenfrequencies slightly lower than the unperturbed values and independent of the area of the load so long as it is small compared to the area of the membrane. It is shown that this result is incorrect because of an invalid initial assumption about the amplitude of vibration of the load. Actually the perturbed frequencies are slightly higher than the unperturbed values, depend upon the area of the load, and approach the unperturbed values as the load approaches point mass. In addition a very low frequency mode exists whose frequency approaches zero as the load becomes smaller in area; this mode represents a perturbation of the trivial zero‐frequency solution in the unperturbed case. The special case of a circular membrane loaded at the center is discussed in some detail.

Signals in a Borehole Due to Plane Waves in the Solid
View Description Hide DescriptionThis paper presents a theory describing the acoustic waves set up in a fluid‐filled borehole by the passage of plane elastic waves in the surrounding solid. It consists of a mathematical development of the following process. A stress in the solid around the borehole will in general cause the hole to contract or expand. A contraction compresses the fluid and causes pulses to radiate in both directions as tube waves. At some observation point, one of these pulses is observed after a delay due to the propagation as a tube wave. A complex wave in the solid is expressed as a combination of stresses distributed along elementary lengths of the borehole, and the total acoustic wave received at a point is expressed as the summation of elementary pulses arriving after suitable delays. The expressions derived give pressure or fluid particle velocity in terms of motion or stresses in the solid for plane compressional waves and plane shear waves arriving at any angle. The method can be extended to the case of a spherical wave cutting the borehole.

Seismic Model Study
View Description Hide DescriptionA method has been developed for studying seismicsound pulses in reduced scale models which simulate geophysicalseismicexploration methods. Use is made of a tank of water for transmission of the acoustic wave from a source to a faulted limestone stratum and return to a pressure sensitive receiver.
Results obtained demonstrating the geometric aspects of the propagation, reflection, refraction, and diffraction of sound pulses are described and illustrated on accompanying plates.

Wave Propagation in a Randomly Inhomogeneous Medium. I
View Description Hide DescriptionThe propagation of sound pulses from a point source in a medium where the index of refraction varies randomly is studied by means of the Born approximation to the wave equation. The coefficient of variation (standard deviation of the amplitude of a series of pulses, expressed as a percentage of the mean amplitude of the series) is evaluated for pulse lengths short compared with the time in which the refractive index varies significantly, and for ranges large compared with the wavelength of the sound. The results are in agreement with the experiments of Sheehy.

Acoustic Streaming at High Reynolds Numbers
View Description Hide DescriptionThe apparent discrepancies between the observations of Andrade and Schlichting and those of Carrière with regard to the direction of acoustic streaming near obstacles has been reexamined. It is pointed out that the geometry of the streaming is determined by the two dimensionless parameters and s/a, where R is the Reynolds number,U _{0} the velocity amplitude of the incident wave,a the characteristic length of the obstacle (radius of cylinder), v the kinematicviscosity and s the displacement amplitude of the incident sound wave. It is found that the Andrade‐Schlichting observations correspond to large values of R (∼1000), whereas the Carrière observations correspond to small values of R (∼10). The present paper deals specifically with the theory for large R and extends the work of Schlichting to discuss the distortion of the flow pattern as a function of the sound intensity. The case corresponding to small Reynolds numbers is treated in an accompanying paper. The results obtained are found to be in agreement with experiments.

Acoustic Streaming at Low Reynolds Numbers
View Description Hide DescriptionThis paper is a continuation of an analysis of acoustic streaming begun in a previous paper where streaming at high Reynolds numbers (order of several hundred) was treated. The corresponding problem for low Reynolds numbers (order of ten) is now considered, and it is shown that the flowpattern obtained around a cylinder in a sound field is opposite to the one corresponding to high Reynolds numbers. The Reynolds number is defined as R = U _{0} a/v, where U _{0} is the particle velocity in the incident sound wave, a is the radius of the cylinder, and v is the kinematicviscosity. The two types of flow associated with different values of Reynolds numbers seem to correspond to the two types of circulations that have been experimentally observed and reported in the literature.

Acoustic Streaming Equations: Laws of Rotational Motion for Fluid Elements
View Description Hide DescriptionIt is shown that the third‐order differential equations commonly used in connection with acoustic streaming are special approximations to the law of rotational motion for a fluid element. An expression is derived for the torque exerted by stresses on a spherical element of fluid, about its center of gravity. The average torque in a steady‐state sound field consists partly of (1) a sonic torque, exerted by the sound field and partly of (2) a viscoustorque due to the induced steady flow. Expressions are also derived for the instantaneous rate of increase of moment of momentum of a spherical fluid element, due to angular acceleration, expansion and shearing. Interpretation is given to individual terms in various streaming equations. In general, any field consisting of superposed elementary waves will give rise to a nonzero distribution of sonic torque. In the special case of a directional source the distribution is similar to that of the gradient of the magnitude of radiation pressure.