Illustration of subhyoidal air sac (left) and lateral ventricular air sac (right) and roughly representing the anatomy of the red howler monkey and siamang, respectively. Note that the howler monkey in reality also has two lateral ventricular sacs, but these are omitted to better illustrate the subhyoidal air sac. Also note that in the siamang the two lateral ventricular air sacs have merged to one sac (the septum is a vestige of the wall between the two sacs).
Schematic representation of air sac, with modeled factors on the left and the lumped element electrical circuit on the right. Elements that are non-negligible are indicated in boldface. Values for elements of the circuit are given in the text.
Free body diagram for wall motion. Note that although damping and stiffness are generated inside the wall, only the component parallel to the wall movement (due to the wall’s curvature) is considered.
Derivation of from generalized Hooke’s law. (A) shows the equations for generalized Hooke’s law, where are the stresses (force per unit area) along the three axes. (B) shows its application to one-dimensional stretching, and obtains one-dimensional Hooke’s law. (C) shows its application to two-dimensional stretching with constant strain in all stretching directions and obtains the relation between Young’s modulus, Poisson’s ratio, and .
Impedances for frequencies between 100 and 2000 Hz for the different elements of the lumped element model. The values of (dotted line) and (solid line) in the graph from left are given (from bottom to top) for soft, cartilaginous, and bony tissues.
Absolute value of the impedances of an example air sac of the dimensions given in Table I with soft, cartilaginous, and bony walls. Both the horizontal and vertical scales are logarithmic. Note the peaks and the zeroes.
Impedances of the finite element air sac models. Air sac dimensions are as given in Table I . Note the similarity for lower frequencies to Fig. 6 . Also note that extra pairs of peaks and zeros, as well as extra isolated peaks, appear at higher frequencies in a very similar way for the three wall types.
Radiated power (given a constant volume velocity source, and including power radiated from the air sac and the mouth) of three different vocal tracts. From above to below, [a], [ə], and [y] are shown. Fat gray dotted lines indicate tracts without air sacs. Solid gray lines indicate tracts with soft-walled air sacs, dashed black lines tracts with cartilaginous air sacs, and solid thin black lines tracts with bony-walled air sacs. Exact dimensions are given in the text. Black lines represent tracts with air sacs, and gray lines represent tracts without air sacs.
Ratio of power radiated through the air sac to power radiated through the mouth for the three different wall types and for air sacs connected to the straight vocal tract. Note that at most frequencies radiation through the mouth dominates, but that at the low-frequency peaks, radiation through the air sac dominates for soft and cartilaginous walls.
Nomogram to calculate the resonances of an oral tract (a straight tube) with an air sac. The narrow gray line represents the negative of the vocal tract susceptance, the broad gray line the soft tissue air sac susceptance, the dashed black line the cartilaginous air sac susceptance, and the solid black line the bony air sac susceptance. The dotted line represents zero susceptance (absence of a parallel impedance). Resonances occur where the lines intersect. Tract and air sac dimensions are given in the text.
Models used in the validation experiment. (A) Perspex models. The vertically displayed model is the air sac. The horizontally displayed models are the vocal tracts. Top row are the [a] models, middle the [ə] models, and bottom the [y] models. Models without air sac are on the left, and models with air sac attachment on the right. (B) Red howler monkey model (the air sac is not spherical because the ratio between area and volume does not correspond to a sphere; at the frequencies involved, exact shape does not matter, only the area and the volume are relevant). (C) Siamang model. All models are to scale. Vocal tracts are depicted horizontally and air sacs vertically. For all models, the glottis is on the right, and the mouth is on the left. Note that the siamang model is closed at the mouth.
Spectra and spectrograms of (A) the red howler monkey and (B) the siamang. Resonances are indicated with arrows. It is indicated in the spectrograms from which part of the signal the spectrum was calculated. Note that in the paper, only the siamang boom is investigated, while in the spectrogram, also the high pitched part of the call (the “shriek,” not analyzed here) is shown (to the right). Also note that there is considerable variation in the howler monkey call (especially in the presence or absence of the resonance around 1700 Hz), while only one part of its call is modeled.
Comparison of calculated (solid lines) and measured (gray lines) spectra of the Perspex models without (left column) and with air sacs (right column).
Radiated power of the “howler monkey” (dashed line) and the “siamang” (solid line) models. For reference, the radiated power of a howler vocal tract without an air sac is also given (gray line). As in the siamang radiation was exclusively through the air sac, only radiated power from the vocal tract with air sac can be depicted. Details about the models can be found in the text.
Constants and parameters used in the lumped element model. Constants taken from Flanagan, 1965 (Sec. 3.25).
Frequencies (in hertz) of the lower peaks of tracts with air sacs, and of the first and second resonances of tracts without and with air sacs, as well as the shifts in frequency, caused by the soft-walled air sac. Peaks caused by the air sac are indicated with , peaks caused by the vocal tract with .
Dimensions of the Perspex models without air sacs, used for the measurements. Sections are numbered from the glottis.
Dimensions of the Perspex models with air sac attachment. Tubes are numbered from the glottis. The column labeled branch indicates the distance between the glottis and the center of the tube connecting the air sac. Due to the connection between the air sac and the vocal tracts, the neck consists of two tubes with numbers 0 and 1. The air sac body is tube number 2.
Values for resonance frequencies of the Perspex models as calculated by the lumped element model, the finite element model, and as measured from the real models. For models without air sacs, only the transmission line model is used, so only one calculated value and the measured value are given. For models with air sacs, the values are given in the order lumped element model/finite element model/measured value.
Article metrics loading...
Full text loading...