Chapter 15, Problem 15.80PP

BIO WAVES ON VOCAL FOLDS. In the larynx, sound is produced by the vibration of the vocal folds (also called “vocal cords”). The accompanying figure is a cross section of the vocal tract at one instant in time. Air flows upward (in the +z-direction) through the vocal tract, causing a transverse wave to propagate vertically upward along the surface of the vocal folds. In a typical adult male, the thickness of the vocal folds in the direction of airflow is d = 2.0 mm. High-speed photography shows that for a frequency of vibration of f = 125 Hz, the wave along the surface of the vocal folds travels upward at a speed of v = 375 cm/s. Use t for time, z for displacement in the +z-direction, and λ for wavelength.

15.78    What is the wavelength of the wave that travels on the surface of the vocal folds when they are vibrating at frequency f? (a) 2.0 mm; (b) 3.3 mm; (c) 0.50 cm; (d) 3.0 cm.

15.79    Which of these is a possible mathematical description of the wave in Problem 15.78? (a) A sin[2πf(t + z/v)]; (b) A sin[2πf(t − z/v)]; (c) A sin(2πft)cos(2πz/λ); (d) A sin(2πft)sin(2πz/λ).

15.80    The wave speed is measured for different vibration frequencies. A graph of the wave speed as a function of frequency (Fig. P15.80) indicates that as the frequency increases, the wavelength (a) increases; (b) decreases; (c) doesn’t change; (d) becomes undefined.

Figure P15.80