In the determination of electromechanical parameters of a piezoelectric vibrator having low figure of merit or low Q by the resonance-antiresonance method, some corrections are necessary to obtain reliable values. In the present paper, some approximate formulas are proposed to make corrections in terms of γ' and β (defined by eqs. (7) and (8)) or of Y_m and β. The vibrator is described by the admittance (1) or (2). The dielectric loss angle φis assumed to be independent of frequency. In the half-width method and the equivalent-resistance method, the formulas [I], [II] and [III] are usually used to determine the parameters. For a given set of K, γ and φ, eqs. (5) and (6) give x_m, x_n and x_1, x_2. Errors of [I], [II] and [III] are obtained from the calculation of the ratios to true values (eqs. (9), (11) and (13)), and the results are shown in Figs. 1 and 2, where the exact solutions are also shown. The coordinates are chosen so as to be represented by observables. In ξ3, approximate correction formulas are derived on the basis of the through-the-center approximation. The geometrical configurations are shown in Fig. 3. The deviations of w_m^2 etc. from w_0^2 can be determined by tan φ_m etc. , as shown by (18) and (21). In the half-width method, a series of equations from (23) to (39) produce a set of approximate formulas of correction [IV・1]〜[IV・3], where X and Z are given by (40). In the equivalent-resistance method, a parameter p of (41) is introduced instead of Y_m. Calculations from (42) to (56) give correction formulas as shown in [V・1]〜[V・6]. The errors of [IV] and [V] are found not to be ignorable, therefore some trials are made in 3. 3 to improve these formulas. Examination of error distributions against w leads to the formulas [VI] and [VII]. The fractional errors of [VI] and [VII] are shown in Fig. 4. They are nearly within a few percent over the practical ranges of w-1 and 1/X or 1/ξ. Accordingly, the approximate formulas [VI] and [VII] are found to be of practical use.
One of the most important subject in the study on prosodic features of speech is how each of laryngeal control and expiratory control contributes to the changes in fundamental frequency and intensity of the glottal sound, and how these physiological controls relate to linguistic informations such as accent, intonation etc. . This paper reports "thyrometer", an optoelectric device for observing the laryngeal control in speech through the vertical movement of the larynx. A small mirror is put on the skin surface near the process of thyroid (or cricoid) cartilage of the speaker, and the incident light beam is projected on it from the front in the mid-sagittal plane. The vertical movement of thyroid (or cricoid) cartilage tilts the mirror, and swings the reflected light beam vertically in the mid-sagittal plane. The reflected light beam passes through a mask whose transmission coefficient varies along the vertical direction, so that the swinging angle of the beam is converted into the variation of light intensity. Then the transmitted light beam is focused through a convex lens on the photocell placed at the image distance of the mirror. Consequently, the vertical movement of the thyroid (or cricoid) cartilage is converted by this device into change in voltage (Fig. 1 and 2). When the mirror is put on a suitable position, a monotonic relationship is maintained between the swinging angle of the reflected light beam and the vertical movement of the thyroid (or cricoid) cartilage (Fig. 3). This method allows a highly sensitive recording of the vertical movement of the thyroid (or cricoid) cartilage in speech almost free from the obstruction of utterance with the simpler device. The time variation of the vertical movement of the larynx ("thyrogram") corresponds well with the fundamental frequency contour in the speech sample in which the stepwise change in pitch is considered to be attributed mostly to the laryngeal control (Fig. 7). It is noticeable that the thyrogram shows integrated rise and differentiated fall suggesting rather slow motion of laryngeal muscles in the rise of pitch and quick motion in the fall of pitch. In the utterances with word accentuation of Japanese (Fig. 8), the peak of the thyrogram appears near the end of the accented more in each word, and the thyrograms show the common underlying laryngeal control for the words having the same accent pattern, in spite of the fact that the fundamental frequency contours are interrupted at the unvoiced part and influenced by the articulation of the vocal tract and/or glottal gestures for consonants. The thyrograms also show the common underlying laryngeal control for the utterances with similar intonation of Japanese interrogative sentences (Fig. 9). In the differentiated thyrogram, active rise of the larynx can be seen at the beginning of the utterance and at the interrogative in the end of sentence. In the utterances of the Four Tones of Standard Colloquial Chinese, the thyrograms show the characteristic laryngeal control of each kind of tones (Fig. 10). Also observed with this method are the effect of some glottal gestures for the utterance of consonants and that of the articulation of vocal tract for each vowel on the movement of glottis, though the amount of the movement is less than that caused by the pitch control (Fig. 5 and 6). The neuromuscular coupling between the vertical movement of larynx and the function of laryngeal muscles controlling the fundamental frequency of glottal sound was examined based on the EMG data (Fig. 11) and the anatomical structure of larynx (Fig. 12). , The thyrohyoid muscle seems to relate to the pitch rise as well as upward movement of larynx while the sternohyoid and the sternohyoid muscles to the pitch fall as well as downward movement of larynx, although the activity of these extrinsic laryngeal muscles are considered to be a secondary support for pitch control.