Question

1. The vocal tract is a resonator and the transmission of sound is highly de- pendent on frequency. The vocal tract has four or five important resonance frequencies called formants. The formant frequencies are determined by the shape of the vocal tract. Assume that the vocal tract can be modeled as a tube, closed at the glottis and open at the lips. The effective length of this tube in the average adult male is about 17.5 cm. Estimate the frequencies of the first four formants. Take the temperature of air inside the mouth to be 32°C.

Answer 1

VA y het 'L' be the length of the tube. (one end closed tube) da funt farment, L= 2 2 = 4 11 + = 6 for suund formant, L= 2 + 2 = 3 7 3 1 1 - fz = 310 for 3rd formart, L2 2 + 2 + 2 = 57 - 50 = fg = 3 for 4th formart, Licht & + 2 + 2 = 7 7 7 6 = fq. 7 ye speed of sound, e (ar 32²) = 331-3+0.606x32 = 350.7mfree L2 17.5 un 20-175 => f, 350-7 350.7 - 4x0.175 501 Hz 3x350.7 = 1503 Hz 4x0.175 5x350.7 4x0.175 - 2505 Hz ty = 7x 350.7 3507 Hz 4x0.175