Volume 33, Issue 5, May 1961
Index of content:
33(1961); http://dx.doi.org/10.1121/1.1908724View Description Hide Description
A criterion for the maximum radiated power delivered by a high‐efficiency piezoelectrically driven free disk, vibrating in the first symmetrical mode, has been developed. The maximum power emitted from such a transducer is necessarily limited by maximum stresses and strains to which the disk is subjected when undergoing transverse vibrations. A complete solution of the stress and strain distribution is given for this mode of vibration. Maximum values for these stresses and strains occur at the center of the vibrating plate. Assignment of a safe stress level, dependent on material, which the center of the vibrating plate must not exceed, then yields a unique value of maximum center velocity at which disk fracture occurs. The maximum power criterion is then established by the maximum safe center velocity, which is shown to be independent of plate geometry, and the radiation resistance of the disk in its operating medium. Experiment shows, as anticipated, that fracture occurs at the geometric center of the vibrating plate, with power values consistent with the theory.
33(1961); http://dx.doi.org/10.1121/1.1908726View Description Hide Description
This paper gives a brief investigation of the concept of the acoustic bearing, the force of which is based on radiation pressure of a resonating sound wave. Of the principal configurations possible, a cylindrical geometry with plates on the ends of the cylinder was considered to be the most suitable. Output ratios of the order of 2640 d/w are shown to be obtainable. Experimentation reached a resonant amplification of 80; ways are shown by which amplifications of around 100 can be achieved. Beyond that internal absorption losses and cavitation present formidable obstacles which, at this point, cannot be overcome.
33(1961); http://dx.doi.org/10.1121/1.1908728View Description Hide Description
An analysis of the voices of sopranos, ranging from singers without any education to artists of world fame, shows a distinct correlation between level of training and vibrato of the voice. Furthermore, analysis of the voices of singers performing in rooms with short reverberation time shows that education is important for the ability to sing correct pitch in words of more than one syllable when the syllables have different pitches. In the analysis of 66 sustained notes, some irregularities were observed in the frequency variations of the overtones. A series of recordings was carried out to detect a plausible reason for these irregularities. The results of various methods of analysis confirm the author's assertion that the sustained note from a highly trained soprano may have parts where the complex wave representing the note is not composed of harmonics.
33(1961); http://dx.doi.org/10.1121/1.1908730View Description Hide Description
It is known that standard procedures used by piano tuners result in a “stretched” scale (i.e., upper tones higher and lower tones lower than the equally tempered scale). Although there was anecdotal evidence of the desirability of this stretch (largely natural consequence of tuning by beats) it had not been formally demonstrated. Therefore recorded tonal and chordal sequences from a small upright piano, tuned to a typical empirical stretched scale by means of a visual device, were compared with similar sequences from the same piano (1) tuned to strict equal temperament (again by means of the visual device), and (2) tuned by a factory “fine tuner” (by the conventional auditory method). Strict equal temperament was unequivocally rejected both by musically oriented research engineers and by music students. Sequences covering the entire pianoscale gave the most pronounced preferences.
33(1961); http://dx.doi.org/10.1121/1.1908732View Description Hide Description
Two experiments were performed to investigate one facet of the question of discriminability of melodic sequences in just intonation and equal temperament. First an ABX test was given to 20 listeners, in which prerecorded ascending diatonic scales of each type were used. Two widely different timbres were used, one flutelike and the other spectrally complex. Only three subjects gave results significantly different from chance. A second experiment employed scales deviating from equal temperament in a manner similar to the just scale, but varying in amount from −6 to −30 cents on the third, sixth, and seventh steps (mi, la, and li). These were compared to equally tempered scales by both ABX and AX procedures. Results showed that the maximum difference between the just and equally tempered scales (16 cents) lies just below the “ABX threshold,” but above the “AX threshold.” It is significant that music students used here (admittedly well conditioned to equal temperament) said that when they. were certain of a discrimination, it was because one of the scales contained tones which were “too flat.”
33(1961); http://dx.doi.org/10.1121/1.1908734View Description Hide Description
According to an acoustical theory of speech production, the spectra of voiceless fricatives can be characterized by poles and zeros whose frequency locations are dependent on the vocal‐tract configuration and on the location of the source of excitation within the vocal tract. The locations of the important poles and zeros in the spectra of fricatives can be determined by a matching process whereby comparison spectra synthesized by electric circuits are matched against the spectra under analysis. This method has been used to determine the frequencies and bandwidths of the important poles and zeros for several versions of /f/, /s/, and /∫/. Based on these findings, a simplified electrical model is developed for the synthesis of voiceless fricatives. The model consists of a noise‐excited electric circuit characterized by a pole and a zero whose frequency locations can be varied. Stimuli generated by this model, both in isolation and in syllables, are presented to listeners for identification. The results of the listening tests are consistent with the data from the acoustic analyses and with the findings of other investigators.
33(1961); http://dx.doi.org/10.1121/1.1908736View Description Hide Description
An acoustic analysis of the rapid fluctuations that occur in the fundamental excitation rate, or “pitch,” of normal speech was conducted with a sample of six male speakers of American English, who each read a neutral test sentence in certain “emotional” modes. i.e., as a question, an objective statement, a fearful utterance, a happy utterance, etc. A statistical analysis of the durations of approximately 7000 pitch periods was performed with an IBM 709 computer. This analysis revealed that for all possible samples consisting of three consecutive periods, the duration did not remain constant, within ±0.1 msec, in 86% of the cases. The data also showed that the magnitude of the difference between the durations of adjacent periods was greater than 0.6 msec 20% of the time and greater than 1.0 msec 15% of the time. The magnitude of this difference increased with the duration of the periods until their duration reached 6 msec. The difference was independent of the period duration for periods longer than 6 msec. Somewhat greater differences between the durations of successive periods occurred in those samples associated with the onset and end of voicing and sudden spectral shifts. Smaller differences occurred with certain of the emotional modes that seemed to require greater conscious vocal control in their production.
The output of the glottis often seemed to be like that of an oscillator with considerable overshoot. In 38% of the cases it produced a sequence of alternately short and long duration periods. The durations of adjacent periods were not correlated. The durations of alternate long and alternate short periods, however, were highly correlated, suggesting a hysteresis effect in which the duration of each period is determined with respect to the preceding period in a quasi random manner within a 2‐msec range.
33(1961); http://dx.doi.org/10.1121/1.1908738View Description Hide Description
Liveness is a quality of sound correlated with room volume, reverberation time, and distance between the sound source and listener (or pick‐up device). In this study, speech samples of varied liveness were obtained by mixing, in controlled ratios, the direct output of the talker's microphone and an output passed through a 9×7.5×6 ft reverberation chamber. In preliminary laboratory tests, the materials consisted of PB words, short phrases, and connected discourse; and varied from very low to high liveness values. The main tests were of an applied nature. Lists of sentences of low and zero (dead) liveness were transmitted over VHF radio and presented over earphones to 19 listeners in a series of intelligibility and preference tests. These lists were also presented to listeners in 105 db SPLhelicopter cabin noise. The results indicated that the live speech was less intelligible and less preferred.
33(1961); http://dx.doi.org/10.1121/1.1908740View Description Hide Description
Aspects of wave propagation of particular importance for the measurement of elastic moduli of solids are first reviewed. Experimental techniques are then discussed, with notes on the suitability for a given application and on factors affecting the accuracy of results. Literature references to the more detailed descriptions are listed.
33(1961); http://dx.doi.org/10.1121/1.1908742View Description Hide Description
Theoretical results are presented which relate the Q factors (internal friction) of solid resonators to two loss parameters λi and μi. The latter are assumed to be characteristic of the energy loss in the homogeneous, isotropic material constituting the resonators. Derivations start from the appropriate frequency—or velocity dispersion—equation in which complex elastic constants, and , are substituted. The following cases are treated: torsional, fundamental longitudinal and fundamental bending modes of solid cylinders, and radial modes of solid and hollow spheres. Deviations from constancy of Q are found in regions where velocity dispersion occurs. Computed results are tabulated which show the dependence of Qμ, upon λ1/μ1 (range 0.1–10) and the propagation factor τ (range 0–5 for cylinders); these apply to duralumin. Similar computations are used to interpret experimental results on polystyrene reported by Biesterfeldt, Lange, and Skudrzyk (see reference 22 in text), and an inconsistency is found in the values of λ i calculated from the fundamental longitudinal and the fundamental bending modes of rods.
33(1961); http://dx.doi.org/10.1121/1.1908744View Description Hide Description
Two elementary problems of guided elastic wave propagation—a point source of SH waves in a free solid plate, and an arbitrary distribution of torsional stress across a normal section of a solid free cylinder—are considered, and exact transient solutions derived.
33(1961); http://dx.doi.org/10.1121/1.1908746View Description Hide Description
The flexural vibration of an infinite elasticbeam which is excited by a localized harmonic driving force and attached over its entire length to a thin elastic plate of infinite extent is investigated theoretically. The results are expressed in terms of two parameters, kbL and r. The parameter kbL describes the frequency dependence and degree of beam‐plate coupling; and the parameter r is the ratio of flexural wave velocity on the plate to that on the beam. For r<1, strong radiation into the plate is possible, while for r>1, plate excitation is localized near the beam. In geometries of practical interest, the strong radiation case prevails. Small deviations in the input admittance of the beam from that of a free beam are initially obtained by employing a perturbation procedure which is valid in the limit kbL≫1, the relevant range for geometries of practical concern. In addition, a variational principle for the admittance is constructed and shown to yield the results of the first‐order perturbation solution when the displacement of a similarly excited free beam is used as a trial function. At very high frequencies the input admittance is found to approach that of a free beam, while at lower frequencies it is found that the plate adds an additional stiffness susceptance to the input admittance. For a typical beam‐plate geometry it is found that the beam is affected by the plate for all forcing frequencies below about 5000 cps and may be estimated by the results of the present calculation down to a few hundred cps.
33(1961); http://dx.doi.org/10.1121/1.1908748View Description Hide Description
An infinite plate to which a narrow infinitely long beam is attached rigidly and continuously may be considered as an idealization of some typical flight vehicle structures. Reflection, transmission, and near‐field effects, associated with a straight‐crested flexural wave impinging on one side of the beam, are presented as functions of the properties of the plate and beam and interpreted in terms of trace matching of the flexural waves in the plate with flexural and torsional waves in the beam. The concepts of dynamic stress and strain concentration factors are discussed, and upper bounds on these factors are given. Some implications pertaining to the design of beam reinforced panel structures with favorable fatigue properties are pointed out.
33(1961); http://dx.doi.org/10.1121/1.1908750View Description Hide Description
Formulas for the attenuation of bending waves that travel over a beam‐plate system, containing one or several beams, are derived and compared with measurements. It is found that one beam gives an attenuation which is very small near the resonances of the beam and rather high elsewhere, but in the average over wide frequency bands the attenuation appears to go nearly like the square root of frequency. The addition of beams of the same material and dimensions does not give an appreciable increase in attenuation. Formulas for the force impedance and mean‐square velocity of beam‐plate systems are also given. Finally, the damping of a beam by a plate attached to it is discussed.
33(1961); http://dx.doi.org/10.1121/1.1908752View Description Hide Description
Sinusoidal vibration has practical value as a substitute for random vibration in equipment qualification testing. How and when to employ a sinusoidal substitution is discussed in this paper. In particular, a damage criterion is discussed, which relates the number of sinusoidal peaks occurring while passing through a resonance to the number of random peaks exceeding a specified amplitude value.
Formulas are given for the sine‐random response relationship, with formulas and a diagram for the random test duration to be used with the amplitude relationship.
33(1961); http://dx.doi.org/10.1121/1.1908754View Description Hide Description
The response of a coupled two‐degree‐of‐freedom system to white noise excitation is obtained analytically for a wide variation of the dimensionless parameters of the system. The interrelations of these parameters on the response are illustrated and shown to be very significant when the uncoupled natural frequencies of the system are of the same order. The limitations of approximation methods based on single‐degree‐of‐freedom system or uncoupled two‐degree‐of‐freedom system models are indicated. The applicability of the study to dynamic vibration absorber principles is evident. The responses are compared to previously published results.
33(1961); http://dx.doi.org/10.1121/1.1908756View Description Hide Description
An experimental study of the scattering of acoustic energy from solid metal spheres in water has been carried out in the frequency range 50–150 kc and with a range of sphere sizes from 1 to 7 in. in diam, giving values of ka (acoustic radius) from 4.1 to 57. Data are presented which show the scattered pulse formation for pulses which are short compared to the sphere and for pulses which are long compared to the sphere as a function of frequency, of scattering angle, and of sphere composition. The study shows that the spheres cannot be treated as rigid bodies since an appreciable amount of energy penetrates the surface and results in a complicated echo structure for the scattered signal. The back‐scattered target strength of spheres for short pulses (and considering only the surface‐reflected pulse) is essentially constant with frequency for large ka, and is slightly less than the theoretical value for rigid spheres. For pulses which are long compared to the transit time across the sphere, the target strength fluctuates as much as 30 db for small changes in frequency. For short pulses the angular distribution of the scattered energy is fairly uniform over the back 180°, but this is not true for long pulses.
Factors that Determine the Equivalent Noise Pressure, Free‐Field Voltage Response, and Efficiency of a Transducer at Low Frequencies33(1961); http://dx.doi.org/10.1121/1.1908758View Description Hide Description
The physical properties and dimensions that determine the equivalent noise pressures of several different shapes of piezoelectric transducers are examined. Expressions for the equivalent noise pressure, free‐field voltage response, and electroacoustical efficiency at low frequencies—those frequencies for which the free‐field voltage response is flat—are obtained in terms of generally known or easily measured parameters. The results indicate that at low frequencies a well designed hydrophone should have an equivalent noise pressure well below zero sea‐state ambient. It is emphasized that the free‐field voltage response is not an indication of the ability of a hydrophone to measure low‐level signals, but that either the efficiency or the equivalent noise pressure is an essential indication of this ability.
33(1961); http://dx.doi.org/10.1121/1.1908760View Description Hide Description
A sound intensity field that is influenced by refraction of high frequency sound in a high‐frequency internal wave is compared with the intensity field in the same medium with no internal wave on the thermocline. Ideal ocean mediums composed of three distinct layers are assumed for both cases. The surface layers have no sound velocity gradient, and the other two layers in both mediums are characterized by linear sound velocity gradients. Properties of the internal waves are similar to those observed off the coast at San Diego, California, in the summer months. The results show that narrow zones of high intensity and broad zones of low intensity alternately occur over a range as predicted by an earlier theory. In the first case (no internal wave in the medium 1, contrasts in the intensity of about 5 db occur over distances of one internal wavelength or less. In the second case (an internal wave in the medium), intensity contrasts of as much as 22 db occur over the same distance.
33(1961); http://dx.doi.org/10.1121/1.1908762View Description Hide Description
Experiments on propagation and compression of pulses in an acoustic waveguide are described. A water filled channel of 32 ft length with pressure release surfaces is used as an acoustic waveguide with a cutoff frequency fc =13.5 kc. Measurements on transient waveforms and on the dispersion curve of the guide in the frequency range between 13.5 and 26 kc are reported. In the pulse compression experiments the wave‐guide is used as a “matched filter” with a frequency‐dependent delay time. A frequency modulated input pulse of 12.6 msec length is compressed into an output pulse of shorter duration and of higher peak amplitude. The frequencies in the input pulse vary from 14 to 22 kc. A time compression ratio of 52.5:1 and a peak amplitude gain of 18.6 db are achieved experimentally. The detection of a pulse in the presence of noise for an input signal to noise ratio of −20 db is illustrated.