Volume 21, Issue 4, July 1949
Index of content:
The High Frequency Region of the Acoustic Spectrum in Relation to Thermal Conductivity at Low Temperatures21(1949); http://dx.doi.org/10.1121/1.1906512View Description Hide Description
21(1949); http://dx.doi.org/10.1121/1.1906514View Description Hide Description
A small load on a bell usually changes the rapidity of beats and shifts the positions of nodal meridians. A study of the first three partials of one bell leads to the following conclusions. If the antinodal meridian nearest the position at which the load is to be applied is associated with the lower [higher] pitched of two beating components, the addition of the load increases [decreases] the rapidity of the beats, and also shifts the nearest antinodal meridian of the lower component toward the position of the load. Small increases in the load increase these effects.
21(1949); http://dx.doi.org/10.1121/1.1906515View Description Hide Description
An ideally stiff string has overtones ν n , which are sharper than multiples of the fundamental, the inharmonicity being proportional to . This well known theoretical result has been verified by Schuck and Young [J. Acous. Soc. Am. 15, 1, (1943)] for typical strings. It is proposed to improve the tone of a piano string by attaching a small mass, thus lowering the frequency of each normal mode except those for which the mass is at a node. It turns out that for an ideally stiff string, approximate correction of a large number of overtones can be obtained with a single mass suitably located. In the limit of a large mass near the end of the string, the correction is exact for all overtones. A mass of the order of 0.1 g placed a few cm from the end of a typical string adjusts the first eight overtones to within a few hundredths of a semitone, a negligible inharmonicity. Improved tone is expected since the subjective fundamentals derived from difference tones between adjacent partials will show greatly reduced dispersion. The effect of the loading upon tuning would reduced the observed stretching of the octaves to a negligible amount. Deviations from ideal stiffness and the effect of adding two masses are also considered.
21(1949); http://dx.doi.org/10.1121/1.1906516View Description Hide Description
Webster's equation for the approximate formulation of the propagation of sound waves in horns is solved using two methods of approach. The first method considers a transmission line with variable parameters as the electrical analogue of the horn. This approach is specially useful in yielding generalized solutions for horns of finite length. The second method, based on an investigation of the singularities of Webster's differential equation, leads to the discovery of a great number of new families of horns.
21(1949); http://dx.doi.org/10.1121/1.1906518View Description Hide Description
A rigid circular plate was exposed to an essentially plane progressive sound wave, and the sound pressurep at various points on the surface measured relative to the free‐field pressurep 0 in the undisturbed incident wave by means of a small probe microphone. The diffractioneffect |p/p 0| was determined as a function of angle of incidence over a range of frequencies beginning with “long” wave‐lengths and extending into the region where the radius a of the obstacle approximately equals the wave‐length. Expressed in customary notation, , where k is the wave number of the incident wave. Data were obtained for angles of incidence θ = 0, 45, 135, and 180 degrees, where θ is measured with respect to the axis of the obstacle. Similar measurements for θ = 0 and 180° were made for a rigid square plate with side 2a.
Approximate contour maps of the quantity |p/p 0| in decibels have been prepared from the experimental data portraying the pressure distribution on the surface of the plates.
The experimental results are compared with computed values of |p/p 0| obtained from an approximate theory in which an attempt is made to solve the problem in terms of a scattered potential calculated as if the face of the obstacle were surrounded by an infinite baffle. The agreement is quite good on the “illuminated” side of the plates, i.e., for θ = 0 and 45° and on the “shadow” side for θ = 180°. The agreement for 135 degree incidence is generally poor, although the computed values show the trends of the experimental data in many instances. At low frequencies the theory gives values which are somewhat too high on the illuminated side and too low on the shaded side.
The values of |p/p 0| obtained from the exact expression of the diffraction of a plane wave by a disk of zero thickness and for perpendicular incidence are found to be in good agreement with experiment and the approximate theory on the illuminated side (θ = 0) and they agree reasonably well on the shaded side (θ = 180°) for 1⩽ka⩽5. The region near the edge shows discrepancies which are to be expected from the finite thickness of the circular plate (approx. a/12).
It is concluded that the approximate theory mentioned above is capable of predicting the diffractioneffect |p/p 0| on the illuminated side of the obstacles in the frequency range covered by this study for the angles of incidence investigated. On the shadow side the theory can be expected to yield usably approximate answers only for θ = 180°. There are reasonable grounds for the assumption that similar predictions can be made for points on or “near” the surface of “thin” plane obstacles of arbitrary shape and for other acute angles of incidence not too close to θ = 90°.
21(1949); http://dx.doi.org/10.1121/1.1906519View Description Hide Description
A concave reflector can be used to concentrate a beam of plane ultrasonicwaves in the focal region, where the intensity If is much larger than the intensity Ii in the plane wave. When the sound wave‐length is small compared to the dimensions of the beam and reflector, one can use the well‐known Fraunhofer diffraction formulas to calculate the intensity gain, i.e., If/Ii . Expressions are derived for the maximum and average intensity gain in the zero‐order image when the ultrasonic beam is circular or rectangular, together with formulas giving the total intensity falling upon circular or rectangular areas of arbitrary dimensions in the focal region.
21(1949); http://dx.doi.org/10.1121/1.1906520View Description Hide Description
This paper discusses a method of producing high intensity sound waves in liquids. A beam of ultrasonicwaves (4.25 mc, 15 × 12 mm cross section, acoustic power≃2 watts) was focused with an ordinary watch glass (6.8 cm radius of curvature). The intensity in the focal region is large enough to raise an ultrasonic fountain 10 cm high accompanied by a spray of fogdroplets. The distribution of intensity in the focal region was determined by measuring the screening effect of properly placed obstacles. The sound intensity in the focal region and in the plane wave was measured by the radiation pressure on beads of convenient size. The absolute intensity in the plane wave was also calculated from the driving potential and the measured mechanical Q of the crystal, and reasonable agreement was found with the direct measurement. A gain in intensity by a factor of about 70 was measured where simple diffraction theory predicts 74. For the highest voltages used the extrapolated negative peak pressure was 41 atmospheres. No cavitation was observed.
21(1949); http://dx.doi.org/10.1121/1.1906521View Description Hide Description
Piezoelectricultrasonic radiators made in the form of a thin spherical shell radiate spherical sound waves which come to a focus at the center of curvature of the shell, thus enabling the production of much greater ultrasonic intensity in a small locality removed from the radiator than it is possible to obtain directly at the surface of a radiator. It is here shown by ultrasoniclight diffraction pictures of the radiated sound field that the sharpness of focus is limited by wavediffraction in the manner well known in astronomical telescopes and may be calculated by optical diffraction formulas. By the same means the radiation efficiency of different areas of the curved surface is explored and the results compared with theory. The variation of efficiency is, of course, due to the variation of the effective elastic and piezoelectric constants of the differently oriented areas. Calculations are made of the radiation efficiency of a quartz radiator, and it is shown that a greatly improved focusing spherical radiator may be obtained by varying the thickness of the radiator to compensate for the varying frequency constant. Further, superior focusing cylindrical radiators may be obtained by special orientation or by thickness shaping or both.
21(1949); http://dx.doi.org/10.1121/1.1906522View Description Hide Description
The properties‐of certain plastic substances have been examined with the idea of using them to construct solid lenses for focussing ultrasonic radiation. Some experiments are described which illustrate the advantages offered by such lenses. The use of a plano‐cylindrical or a plano‐spherical lens permits a reduction to 1/10 or 1/100 respectively of the energy which must be emitted by a quartz crystal to produce a given intensity of ultrasonic radiation over a given region.
21(1949); http://dx.doi.org/10.1121/1.1906523View Description Hide Description
The description of a lamination design for the magnetostrictive motors of a directional transducer array. The design makes possible the efficient operation of the transducer with a “Q” of 6 under a full water load. Array patterns are presented to show that the laminated motors radiate as plane pistons into the medium.
21(1949); http://dx.doi.org/10.1121/1.1906524View Description Hide Description
Equipment has been built for measuring vibratory displacements of very small mechanical elements such as phonograph styli and piezoelectric crystals. It employs a probe of small dimensions so that virtually point measurements may be made. The probe does not contact the point under measurement and therefore imposes no mechanical load. The variation in capacitance between probe and vibrating surface is used to measure the displacement. Through the use of a built‐in calibrator, the sensitivity may be adjusted electrically for direct meter reading of vibratory displacement without resorting to precise adjustment of condenser plate spacing. Displacement amplitudes of less than 10−6 cm may be measured. The output signal corresponds accurately to the displacement both in magnitude and in phase over a wide frequency range so that complex vibrations are portrayed accurately on a cathode‐ray oscilloscope. The equipment has been calibrated by four independent methods, including a reciprocity method, with close agreement.
21(1949); http://dx.doi.org/10.1121/1.1906525View Description Hide Description
One, two, four, and eight simple tones were presented to listeners against a background of thermal noise. The masked thresholds for the single tones and the various combinations were determined, for different spacings of the tones. In the case of two tones, the improvement in threshold with respect to a single tone was slight or negligible unless the tones were within one critical band, when the improvement increased as the spacing decreased. In the case of four or eight tones all separated by more than a critical band, the improvement was slight (less than 3 db) or negligible, apparently depending on the combination of frequencies.
21(1949); http://dx.doi.org/10.1121/1.1906526View Description Hide Description
A monaural loudness matching technique was used to study differential sensitivity to intensity as a function of tonal duration. The probable error (p.e.) of the loudness matches was used as the measure of differential sensitivity. With one technique, a standard tone of 500 milliseconds duration was followed by a tone of variable duration (10–500 milliseconds) after a silent interval of 50, 100, or 500 milliseconds. In another technique, both standard and comparison tones were of the same duration (10–500 milliseconds) with the same silent intervals between tones as before. (1) When the standard tone was always 500 milliseconds, the p.e. of the loudness matches increased with a decrease in the duration of the comparison tone from approximately 0.60 to 2.30 db, and the length of the silent interval had no effect on the function. (2) When both the standard and comparison tones had the same duration, the p.e. again increased with a decrease in duration; in this case, however, a silent interval of 500 milliseconds caused an increase from approximately 0.60 to 2.50 db while a silent interval of 50 milliseconds caused an increase to only 1.00 db. These differences are explained in terms of two different processes: a dissimilarity effect, and an interference effect. (3) When a standard tone of constant duration is used to obtain loudness matches, the mean of the matches becomes a measure of the loudness of tones as a function of duration. These measures showed a clear distinction between the six observers used. For three observers, the change in duration caused practically no change in loudness. For the other three, changes in loudness as great as 8.5 db were recorded. This order of loudness change agrees with that reported by Békésy, but is considerably less than that reported by Munson. Possible explanations for the differences are mentioned.
21(1949); http://dx.doi.org/10.1121/1.1906527View Description Hide Description
I studied principally the mechanics of the middle ear, summarizing the anatomy and the physiology of the ear. I made Diagram I showing the anatomical structure of the ear, and translated it into physical terms of Diagram II, such as mass, spring, and frictional constant. etc. Thereafter I could get equations showing the mechanics of the middle ear through the Lagrangianequation. The complicated treatment for the kinetic, potential, and dissipation energies of the middle ear elements is for the purpose of expressing my opinion about the function of the middle ear which is partly different from the present contradictory medical views. By using the resultant equations of the motion of the ear and Diagram III (showing the electromechanical structure of the middle ear), I studied the mechanism of the middle ear under an assumption that the frequency characteristic curve of the inner ear is flat in a wide range. This assumption may be deduced from Luscher's experiment of the tympanic loading and hearing curves of men with complete defect of the tympanic membrane but with cochlear nerve intact. However, I do not explain it here, and it will be described in detail in further papers. From theoretical results thus obtained I made some experiments and calculation of the natural frequencies of the middle ear elements.
My conclusions are as follows: (a) The air vibration system of the ear which consists of the external auditory canal, the tympanic cavity, and the antrum can be shown electromechanically by Diagram III. (b) The middle ear has four main peaks of resonance on the hearing curves. (c) The middle ear and cochlea appear to be regarded as a displacement receiver and a pressure receiver, respectively. (d) The tympanic membrance has two important roles: (1) that of composing the vibration of the external auditory canala, of the antrum, and of the air cells of the mastoid process; and (2) that of propagating these vibrations to the ossicles. (e) The non‐linear vibration of the tympanic membrane, the basilar membrane, and the secondary tympanic membrane, produce combination tones. (f) The air vibration system has an important role in understanding speech sounds. Its magnification of the sound intensity is above 50 db in a range from 700 or 800 cycles to 5000 cycles as in Fig. 5a. (g) This work offers a problem of design of a new audiometer, and is available for diagnosis of otological pathology.