Volume 22, Issue 3, May 1950
Index of content:
22(1950); http://dx.doi.org/10.1121/1.1906606View Description Hide Description
The one‐dimensional wave equation is discussed to the second order of approximation by means of a transformation that carries the equation from the Eulerian to the Lagrangean form. Airy's solution to this equation in Lagrangean form has been shown by Fubini to be an excellent approximation to an exact solution of Earnshaw's equation of motion; therefore, Airy's solution is chosen as the basis for much of this discussion. An expression for the local mean hydrostatic pressure in a plane progressive wave is obtained by transforming Airy's solution from particle to local coordinates. In a similar way, the particle velocity in fixed coordinates is shown to possess a time‐independent component proportional to, and in a direction opposite to, the intensity vector This d.c. counter‐velocity is predicted without recourse to viscous forces and is compatible with zero average mass velocity. For a sound pressure level of 151 decibels in air there should exist a steady particle velocity of 1 cm/sec. Small particles suspended in the field can, under certain circumstances, acquire this velocity. An approximate treatment is suggested for handling second‐effects arising from stationary field configurations. The influence of viscosity is discussed qualitatively.
One purpose of this paper is to correlate work in the field which has not so far been published in this country.
22(1950); http://dx.doi.org/10.1121/1.1906607View Description Hide Description
22(1950); http://dx.doi.org/10.1121/1.1906608View Description Hide Description
Many sounds of speech and music more nearly resemble pulsed wave trains than abruptly terminated continuous sounds as used in reverberation measurement. It is therefore not surprising to find that two rooms can differ markedly in acoustical quality even if they appear identical under reverberation analysis which ignores details of short transients.
This paper introduces a pulse statistics point of view which takes immediate account of the pulse‐like nature of common sounds. Fundamentally, the method consists in examining the response of the room to a short pulse. The walls are replaced by an array of image sources (simple images if the walls are hard, or appropriately modified if there is absorption). These image arrays are then considered statistically.
From this approach one can derive such classical quantities as reverberation time and mean free path. One can also analyze the detailed nature of discrete reflections including interference effects, and thus obtain an average correlation between room geometry and the character of its pulse response.
Idealized experiments in a hard‐walled rectangular room are employed to illustrate the essential features of this approach. A point source emits an exponential damped 3600‐c.p.s. wave train of about 2 msec. duration. The received signals are recorded logarithmically on an oscillograph and the system is calibrated for quantitative results. Several dozen discrete reflections can be measured and correlated with calculation. The pulses merge into a more or less continuous background after a time that is calculated and confirmed experimentally. Detailed differences arise according to the positions of the source and microphone in the room.
22(1950); http://dx.doi.org/10.1121/1.1906609View Description Hide Description
The propagation of transient sound waves in bounded one‐ and three‐dimensional regions is studied by means of Laplace transform methods. In the one‐dimensional case, a plane wave is considered propagated down a rigid‐walled tube from a source at one end toward an acoustic termination at the other end. The velocity potential for an arbitrary particle‐displacement input is found as a series, each term of which represents the effect of a reflection from the ends of the tube. In the three‐dimensional case spherical wave from an arbitrary input source is considered, first in an unbounded region, and then in regions containing one wall, three perpendicular walls, and two parallel walls; finally, the case of a point source in a rectangular room is solved. An image method is used, the results being found in the form of a series whose terms represent reflections from individual walls, as well as cross reflections between walls. The terms of the series are in the form of plane‐wave expansions around the image points; these integrals are approximated by the method of steepest descents. In the last section some sample calculations are made for both the one‐ and three‐dimensional systems.
22(1950); http://dx.doi.org/10.1121/1.1906610View Description Hide Description
22(1950); http://dx.doi.org/10.1121/1.1906611View Description Hide Description
Often, the lower normal modes of slim but complicated structures can be computed with sufficient accuracy if the computations are based upon a tapered continuous beam in which the stiffness and inertia of the beam match those of the structure at a large number of points along its length. Shear motions play a dominant role in these calculations. Even with the continuous beam approximation, the numerical computations involved are lengthy and time consuming. An equivalent electric circuit for the beam makes it possible to substitute model experiments for lengthy calculations. It is here shown that such an equivalent circuit can be constructed which is made up of lumped passive components. Given such a circuit, it is then possible to determine experimentally the gross responses of the structure to an arbitrary excitation.
22(1950); http://dx.doi.org/10.1121/1.1906612View Description Hide Description
Some of the more important mechanical design details of a newly developed accelerometer are described, together with their bearing on the dynamic characteristics of the unit. The relationship of acceleration range, sensitivity, and natural frequency for the design is defined, and its properties of selectivity and stability are discussed. Various types of coupling circuits in present use with high and low impedance loads are diagramed, and the possibility of greater zero stability by the use of a low level carrier is noted.
22(1950); http://dx.doi.org/10.1121/1.1906613View Description Hide Description
The scatter in phase which occurs when a beam of ultrasonic radiation transverses polycrystalline medium is here treated as a stochastic process. This approach leads to an attenuation from polycrystallinescattering proportional to the grain size divided by the square of the wave‐length. Whereas prior treatments of this subject are valid for the wave‐lengths either much smaller or much larger than the grain size, the method used here holds best over the intermediate frequency range.
22(1950); http://dx.doi.org/10.1121/1.1906614View Description Hide Description
Investigation of the sound pressure on the axis of the mouth indicates the existence of a point which may be represented as the source of speechsounds. The location of this point is dependent upon the particular speechsound, the intensity with which it is uttered, and upon the frequency components under consideration. Using young, average, male speakers, this apparent source of speech was located for 18 frequency bands covering the portion of the spectrum which contributes to speech intelligibility in each of 38 fundamental speechsounds.
22(1950); http://dx.doi.org/10.1121/1.1906615View Description Hide Description
A hydrodynamical theory is given for a model of the cochlea. The model consists of two channels of varying but equal cross sections. The channels are separated by an elastic membrane with variable dynamical constants. The two channels are interconnected at one end, and the entire structure is rigidly enclosed except for two accessible areas corresponding to the round and oval windows. The equations of motion, continuity including the effect of the membrane, and appropriate boundary conditions are formulated. As a first step toward a complete analysis the non‐dissipative case is considered. Numerical solutions are found using experimental data obtained by G. v. Békésy. Localization phenomena and phase velocities are found to be in broad agreement with experimental data.
22(1950); http://dx.doi.org/10.1121/1.1906616View Description Hide Description
The results of psychophysical tests on the auditory sensory system usually show much more variability than experiments involving only physical measurements of sound waves. This has resulted in the general impression that the variance of measurements of the auditory threshold and other psychoacousticmeasurements is largely due to the inability of the observers to give consistent responses. This paper reports the results of a series of threshold measurements made under carefully controlled conditions and accompanied by search tube measurements of the sound pressures in the ear canals of the observers. The small variances obtained under certain conditions suggest that the large variability oftentimes experienced in psychophysical work is partly due to inadequate techniques for measuring the levels of the stimuli that activate the sensory system.
22(1950); http://dx.doi.org/10.1121/1.1906617View Description Hide Description
In 1939 a symposium was held by the Acoustical Society of America on the measurement of absorption coefficients. In these and other papers, the reverberation chamber method of determining absorption coefficient was analyzed, and explanations for discrepancies between different chambers, and lack of agreement with other methods, were presented in terms of newly developed theory. Since that time, however, practically no progress has been made in the application of this theoretical work. The discrepancies remain unresolved, and the practical problems resulting therefrom have become increasingly serious.
Within recent months, interest in this subject has been strongly reactivated through the attention of three groups, namely, the American Standards Association, the American Society for TestingMaterials, and the Acoustical Materials Association. By closely coordinated efforts, these groups are making a new attempt to develop methods of measuring and rating the absorptive properties of acoustical materials which will yield consistent results in the form most useful for practical engineering work and at the same time are grounded in well‐established acoustical theory.
In the present paper, the general problem is outlined from the viewpoint of the acoustical materials manufacturer. Directions of further development in theory and of experimental attacks are suggested.