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Volume 12, Issue 2, October 1940

Acoustic Impedance and Sound Absorption
View Description Hide DescriptionTheoretical curves for acoustic impedancevs. frequency, obtained by solving the equation for wave motion within the material, are compared with recently measured values of the impedance of various sound absorbing materials. The satisfactory agreement in most cases measured indicates that that for homogeneous materials the effective values of flow resistance, porosity and material density are nearly constant over the frequency range 200 to 6000 c.p.s. This makes it possible to express the whole acoustic behavior of these materials by three constants. The behavior of two nonhomogeneous materials is also discussed. The relation between impedance and the various types of absorption coefficient is discussed, and specific formulas for the coefficients are given in terms of the acoustic impedance. It is indicated that in rectangular chambers, when the sound does not have a random diffusion throughout the room, the decay curve for pressure squared in db, vs. time in seconds, is a broken line, with the initial slope corresponding to a coefficient for normal incidence, and the final slope corresponding to a coefficient for grazing incidence. If enough scattering objects are inserted to make the diffusion of sound complete, so that no standing wave is all grazing or all normal to any surface, then the decay curve is a straight line with slope corresponding to the coefficient defined by Sabine. A formula relating this coefficient to the acoustic impedance is given. The Acoustical Materials Association values of absorption coefficient, used in practice, are compared with the curves of normal and Sabine coefficient, computed from the experimental curves for impedance. It is apparent that above 2000 c.p.s. the A.M.A. values equal the computed Sabine coefficients, indicating sufficient diffusion of sound in the reverberation chambers at these frequencies. Below 500 c.p.s. the A.M.A. values correspond more closely to the normal coefficient, indicating an insufficient diffusion of sound, and that the initial slope of a broken line decay curve is being measured. In these two ranges of frequency, therefore, one can compute the A.M.A. coefficients from the impedance. It is suggested that field coefficients for large auditoriums correspond to the computed Sabine coefficient for lower frequencies than do the A.M.A. coefficients. A simple formula is given for the broken line decay curve in a rectangular room with no diffusion, and is checked by experimental curves. A case of partial diffusion is discussed, where the decay curve is intermediate between the theoretical curves for complete and for no diffusion.

Sound Absorption in Rectangular Ducts
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Transmission of Sound Through Parallel Conduits
View Description Hide DescriptionThis paper is a theoretical study of the passage of sound through a series of similar sections composed of two parallel conduits. The infinite structure and the finite structure with finite termination are examined. The filter is low‐pass and, by varying the cross sections and the lengths, practically as many or as few frequencies as desired, from 0 to 10,000 cycles, can be attenuated. The effect of cylindrical and conical finite terminations is calculated and plotted. The latter graphs indicate that by varying the length of the termination so that its anti‐resonance frequencies fall within attenuation bands, the transmission is very approximately that predicted from the infinite structure study.

The Absorption of Sound in Carbon Dioxide
View Description Hide DescriptionThe absorption was measured by a direct method over frequencies between 22 and 112 kc. A microphone responding to the sound pressure is moved away from a piston source located in a flat surface. The output of the microphone is amplified and recorded photographically. The resulting pressure‐distance curve yields the pressureattenuation coefficient. The measurements were made in carbon dioxide which was carefully dried by passing it through phosphorus pentoxide. The results of the measurements bear out the theoretical work of Bourgin. The lowest value obtained for the frequency at which the absorption per wave‐length μ is a maximum was 30 kc. In order to account for the maximal value of μ obtained experimentally, it is necessary to assume that both the symmetrical valence vibration and the deformation vibration are effective in producing the absorption, and in addition that the second harmonic of the deformation mode also participates in the absorptive process. Velocity measurements made with the same apparatus have shown a reasonable agreement between the dispersion and absorption in carbon dioxide.

The Absorption of Sound in Five Triatomic Gases
View Description Hide DescriptionThe sound absorption coefficients have been measured between 8 and 130 kilocycles for the five triatomic gases , COS, , and . The frequencies of maximal absorption for these molecules were found to be at 20, 153, 287, 379, and 1040 kc, respectively. It was found that for the linear molecules , COS, and a linear relationship exists between the maximal absorption coefficients and the frequencies at which these maxima occur. It was also found (1) that the lower the fundamental frequencies of vibration of the four linear molecules the higher are the acoustical frequencies of maximal absorption, i.e., the shorter are the lifetimes of the energy quanta; and (2) that the sonically activated fundamentals and harmonics of each of the above linear molecules commute and have the same lifetime, with the possible exception of . From the experimental data it was possible to calculate the reaction rates, probabilities of removal of vibrational quanta, the numbers of collisions necessary to remove the quanta of energy, and the numbers of quantum transitions per second. In addition to the above data, a technique is presented which enables one to find the frequencies of maximal absorption for gases when these frequencies occur in a range beyond the scope of the apparatus.

The Absorption of Sound in , COS, and in , Containing Added Impurities
View Description Hide DescriptionWe have investigated the absorptive characteristics of , COS, and as influenced by the addition of certain gases, such as , etc., acting as “catalysts.” These catalysts shift the absorption bands to higher frequencies; the magnitudes of these shifts yield information respecting (1) the frequency at which each pure gas has its maximal absorption, and (2) the nature of the molecular collisions involved, and especially the effectiveness of these collisions in disturbing the vibrational states of the absorptive molecules. The results indicate that at atmospheric pressure and 23°C the absorption maxima for pure , COS, and are shifted in each case by amounts proportional to the concentration of the added catalyst. The addition of one percent of to shifts the absorption band for 2250 kc; similarly, one percent of shifts the band 2460 kc, the COS band 4200 kc, and the band 427 kc. One percent of the other impurities produced shifts which varied from 20 to 1830 kc. Transition probabilities for the above gases have been calculated. These probabilities are characteristic of the colliding pair of molecules.

Symmetrical Sand Figures on Circular Plates
View Description Hide DescriptionIt is shown that Kirchhoff's solution for a circular plate is a special case which gives circles and diameters only. If this solution is generalized, the very intricate figures actually found upon circular plates may be calculated mathematically. In particular, a few figures found by Chladni are computed from the new equations. The methods of computation from the curves of the Bessel functions are outlined briefly.

A Physical Analysis of Distortion Produced by the Nonlinearity of the Medium
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The Interference of Tones in the Cochlea
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Three Mechanisms of Hearing by Electrical Stimulation
View Description Hide DescriptionIt was previously shown that when an alternating electric current is passed through the head via a salt solution in the external ear canal, a normal observer hears a tone which is related to the stimulus by a square law, that is to say, if the sound heard is interpreted in terms of motion of the tympanic membrane, then the displacement of the membrane is proportional to the square of the instantaneous voltage. The writers suggested the hypothesis that the cavity formed by the middle ear acts as an electrostatic transducer. This hypothesis accounted for the square‐law response and for certain quantitative aspects of the results. This hypothesis had to meet the objection, however, that persons without tympanic membranes are able to hear by electrical stimulation. In order to determine the relation between the hearing of normal and operated ears, twenty ears lacking tympanic membranes were stimulated electrically. Eleven ears heard pure tones corresponding in pitch to the frequency of the applied voltage; seven heard a buzzing noise whose character was roughly independent of the stimulating frequency. Examination showed that the pure‐tone response in the operated ears was purely linear, in contradistinction to the quadratic response of normal ears. Hence, under electrical stimulation normal and operated ears hear by means of two distinctly different mechanisms. The square‐law response in normal ears is apparently mediated by an electrostatic action in the middle ear. The linear response in operated ears may or may not be the inverse of the cochlear microphonic. Evidence is presented that direct stimulation of the auditory nerve occurs in those ears which bear a buzzing noise. This result is consistent with a “place theory” of hearing, and it suggests that the “frequency theory” of hearing is untenable even for low frequencies.

Results of the World's Fair Hearing Tests
View Description Hide DescriptionThe hearing test for musical tones which formed part of the Bell System exhibit at the New York and San Francisco Fairs is described. Average hearingacuity and the frequency of occurrence of various amounts of hearing loss are given as functions of age and sex. The relation of hearingacuity to place of residence, economic status and certain other factors is discussed briefly. Data from the two Fairs are used to determine the distribution of hearingacuity in the United States population, subject to certain stated limitations. Accuracy of the test is discussed in relation to ability of visitors to understand the test procedure, disturbing effect of background noise, and calibration of the test equipment. Certain results of the survey are expressed in terms of ear canal pressure and equivalent free field intensity, and on this basis a comparison is made with the results of other surveys of hearing.