Normal vibration frequencies of the vocal ligament

The vocal ligament is the tension-bearing element in the vocal folds at high pitches. It has traditionally been treated as a vibrating string, with only length and longitudinal stress governing its normal mode frequencies. Results of this investigation show that, when bending stiffness and variable cross section are included, the lowest normal mode frequency can more than double, depending on the strain of the ligament. This suggests that much higher phonation frequencies may be achievable than heretofore thought for a given vocal fold length (e.g., nearly 1000 Hz at 50% elongation over cadaveric resting length). It also brings back into the discussion the concept of "damping," an old misnomer for a reduction of the effective length of vibration of the vocal folds by relatively stiff boundary segments known as macula flavae. A formula is given for correcting the ideal string equation for the lowest mode frequency to include bending stiffness and macula flavae effects.