Determination of Smoothed Cross‐Sectional‐Area Functions of the Vocal Tract from Formant Frequencies

1965 ◽  
Vol 37 (6) ◽  
pp. 1186-1186 ◽  
Author(s):  
Paul Mermelstein ◽  
M. R. Schroeder
Keyword(s):  
Vocal Tract ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Formant Frequencies

DETERMINATION OF THE FUNCTION OF THE ROD’S CROSS-SECTIONAL AREA USING VIBRATION EIGENFREQUENCIES

2020 ◽  
Vol 0 (4) ◽  
pp. 19-24
Author(s):  
I.M. UTYASHEV ◽  
◽  
A.A. AITBAEVA ◽  
A.A. YULMUKHAMETOV ◽  
◽  
...  
Keyword(s):  
Cross Sectional Area ◽  
Variable Cross ◽  
Sectional Area ◽  
Longitudinal Vibrations ◽  
Cross Sectional ◽  
Method Error ◽  
Various Boundary Conditions ◽  
Elastic Fixation ◽  
Crosssectional Area

The paper presents solutions to the direct and inverse problems on longitudinal vibrations of a rod with a variable cross-sectional area. The law of variation of the cross-sectional area is modeled as an exponential function of a polynomial of degree n . The method for reconstructing this function is based on representing the fundamental system of solutions of the direct problem in the form of a Maclaurin series in the variables x and λ. Examples of solutions for various section functions and various boundary conditions are given. It is shown that to recover n unknown coefficients of a polynomial, n eigenvalues are required, and the solution is dual. An unambiguous solution was obtained only for the case of elastic fixation at one of the rod’s ends. The numerical estimation of the method error was made using input data noise. It is shown that the error in finding the variable crosssectional area is less than 1% with the error in the eigenvalues of longitudinal vibrations not exceeding 0.0001.

scholarly journals Geometry of the Vocal Tract and Properties of Phonation near Threshold: Calculations and Measurements

2019 ◽  
Vol 9 (13) ◽  
pp. 2755 ◽  
Author(s):  
Lewis Fulcher ◽  
Alexander Lodermeyer ◽  
George Kähler ◽  
Stefan Becker ◽  
Stefan Kniesburges
Keyword(s):  
Vocal Tract ◽  
Wave Model ◽  
Vocal Folds ◽  
Cross Sectional Area ◽  
Inertial Effects ◽  
Sectional Area ◽  
Cross Sectional ◽  
Physical Mechanisms ◽  
Lumped Element ◽  
Geometrical Boundary

In voice research, analytically-based models are efficient tools to investigate the basic physical mechanisms of phonation. Calculations based on lumped element models describe the effects of the air in the vocal tract upon threshold pressure (Pth) by its inertance. The latter depends on the geometrical boundary conditions prescribed by the vocal tract length (directly) and its cross-sectional area (inversely). Using Titze’s surface wave model (SWM) to account for the properties of the vocal folds, the influence of the vocal tract inertia is examined by two sets of calculations in combination with experiments that apply silicone-based vocal folds. In the first set, a vocal tract is constructed whose cross-sectional area is adjustable from 2.7 cm2 to 11.7 cm2. In the second set, the length of the vocal tract is varied from 4.0 cm to 59.0 cm. For both sets, the pressure and frequency data are collected and compared with calculations based on the SWM. In most cases, the measurements support the calculations; hence, the model is suited to describe and predict basic mechanisms of phonation and the inertial effects caused by a vocal tract.

Determination of the cross-sectional area of the indenter in nano-indentation tests

2007 ◽  
Vol 391 (1) ◽  
pp. 118-123 ◽  
Author(s):  
Jeremy McMinis ◽  
Rene Crombez ◽  
Eva Montalvo ◽  
Weidian Shen
Keyword(s):  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Nano Indentation ◽  
Indentation Tests ◽  
The Cross

Determination of cross-sectional area of natural plant fibres and fibre failure analysis by in situ SEM observation during microtensile tests

Cellulose ◽  
2019 ◽  
Vol 26 (8) ◽  
pp. 4693-4706 ◽  
Author(s):  
Hangbo Yue ◽  
Juan C. Rubalcaba ◽  
Yingde Cui ◽  
Juan P. Fernández-Blázquez ◽  
Chufen Yang ◽  
...  
Keyword(s):  
Failure Analysis ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Cross Sectional ◽  
Natural Plant ◽  
Fibre Failure ◽  
Sem Observation

Accurate Measurement on Cross Sectional Area of Single Filaments Using a Desktop SEM

2015 ◽  
Vol 1083 ◽  
pp. 111-117
Author(s):  
Xi Ying Yang ◽  
Ou Yang Ting ◽  
You Qing Fei
Keyword(s):  
Accurate Determination ◽  
Cross Sectional Area ◽  
Morphological Observation ◽  
Sectional Area ◽  
Cross Sectional ◽  
Fiber Properties ◽  
Measurement Results ◽  
Fiber Sample ◽  
Key Parameter

Cross sectional area of single filaments, a key parameter to characterize fiber properties, was experimentally studied using a desktop scanning electron microscope. Three different methods are employed based on the pixel area, averaged diameter and single diameter measurements, respectively. Results have shown that all three methods can achieve accurate measurement results once the axis of fiber sample is kept parallel to the electron beam. Significant errors are generated for the fiber samples with their axis tilted, which may frequently occur as a sample prepared. For circular fibers, a single diameter measured from tilted fibers is sufficient to determine their cross sectional area at high precision with COV values below 1.6%. By selecting an appropriate method, a desktop SEM can serve as a convenient and powerful tool for accurate determination of cross sectional area as well as morphological observation.

Sign in / Sign up

Export Citation Format

Share Document