A Theory of Vibration of the LarynxUniversity of Wisconsin--Madison, 1928 - 54 pages |
Common terms and phrases
air chambers air flow air stream approximately area S2 assumed Bernoulli coupling Bernoulli effect coefficient of q₂ compared to w₂ compression coordinate cord tip decrement dissipation equation 11 equilibrium position flow of air force equations free vibration glottis and vocal glottis mass harmonic content Helmholtz resonator I₁ I₂ imaginary inertia reactance instantaneous jwL₂ kinetic energy L₁ L₂ Lagrange equation larynx linear measured models modulation constant natural frequency necessary to evaluate neglecting the reactions notation pharynx plug of air positive root power series pressure quantities R₁ ¹1 R₁L2 R₂ relatively represented resistance and inertia resistance modulation Ro I1 S₁ S₂ slit width small superimposed small velocity stiffness K₂ sustained oscillation sustained vibration trachea and lungs trachea piston tube turbulence UNIVERSITY OF WISCONSIN upper vocal cavities v₁ velocity of flow vocal cords VOCAL TRACT voice volume of air w₁ w₂² written For simplicity ZOS1 Әт
Popular passages
Page 5 - A positive displacement q^ (outward) of the vocal cords causes an increase in the mass of the plug of air in the glottis and a change in the effective resistance, R, encountered by it. The inertia L\ and resistance R of the glottis are therefore both functions of q«, the displacement of the vocal cords from a mean position, and of the width of the glottis. If further...
Page 27 - The Theory of the Operation of the Howling Telephone with Experimental Confirmation, H.
Page 2 - Fig. 1 — Anterior-Posterior Section of the Larynx. larynx (see Fig. 1) for producing the periodic modulation and the upper vocal cavities, pharynx, mouth and nose for varying the relative harmonic content of sound originating in the larynx. The capacity of the lungs in an adult man is capable of being varied from about two to five liters. The average in quiet breathing is about 2.6 liters. The average expiration of air in quiet breathing is about .5 liter. The rate of expiration of air in medium...
Page 7 - J/g" brass plates, b, fitted on these beveled surfaces so as to leave a slit, S, which was made adjustable in width. A cross-section of this model is shown in c. The bottom of the tube was attached to a large air chamber in which the pressure and velocity of air flow could be regulated and measured. Three shapes of "glottis" were measured. The first had square corners, as shown on Fig. 3c. The second, 3d, was the same as 3c, except that the corners of the lips were rounded. The third, Fig. 3e, had...
Page 14 - ... justification and limitations that it is ignored in the elementary treatment of electrical circuits containing coils with magnetic material and condensers with electrostatic hysteresis. External Reactions of the Trachea and Vocal Cavities on the Larynx So far the modifying effect of the trachea and lungs, as well as the upper vocal cavities, on the motion have not been considered. Before using the equations it is necessary to evaluate these reactions and add them in their proper places. Imagine...
Page 3 - ... 200 cm .'/sec., the lower values obtaining for trained singers. The larynx (see Fig. 1) consists of an irregularly shaped cartilaginous box at the top end of a tube, the trachea, about 12 cm. long by 2 cm. in diameter, leading from the lungs. The larynx contains the vocal cords, a pair of fibrous lips which in vibrating vary the width of the slit called the glottis, between them. The length of the glottis in the adult male averages about 1.8 cm. and in the female 1.2 cm. The width of the glottis...
Page 8 - The second, 3d, was the same as 3c, except that the corners of the lips were rounded. The third, Fig. 3e, had square corners as before, but the slit was about .1 mm. wider in the middle than at the ends. Fig. 3 — Glottis Models. The resistance R is given as the ratio of the product of pressure and slit area to the linear velocity of flow. Measurements were made in each case through a range of pressures such as to give fluxes through the slit through a range of 50 to 200 cm.3/sec. (Stanley and Sheldon...
Page 8 - X 10-6. In these expressions / is the velocity of flow of air through the slit. More careful data taken through a wider range of I and W would undoubtedly have given R in a power series. These formulae are taken to indicate that the resistance of the actual glottis increases faster than a linear function of / and W due to turbulence and may be represented as a single valued function of either displacement of the vocal cords q% (or glottis width) or of air velocity as expressed by a Taylor's series...
Page 1 - ... equations, which describe the vibrations of the complete mechanical system, by means of the Lagrange equations, from expressions of the total instantaneous kinetic and potential energies, the instantaneous forces acting and rate of dissipation of energy. The resulting simultaneous equations relating to the displacements and velocities of the various parts are then studied to find the frequencies of free vibration and the relations which must obtain between the various mechanical parameters of...
Page 2 - ... introduction of simplifying approximations which will be described in the progress 1 Presented before Acoustical Society of America, May 11, 1929. of the discussion. The principal one of these is the neglecting of all reactions of second or higher order, thus leaving a set of linear differential equations. STRUCTURE OF THE VOCAL TRACT The vocal tract consists of three principal parts, the lungs and associated respiratory muscles for maintaining a flow of air, the EPIGLOTTIS FALSE VOCAL CORDS...