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UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
Department of Electrical and Computer Engineering Instructor: Mark Hasegawa-Johnson ECE 537 Speech Processing
Problem Set 2
Fall 2009
Issued: Wed Sep. 2, 2009 Due: Wed Sept. 16, 2009
Reading for problem set 2: Flanagan, Allen & Hasegawa-Johnson 3.1-
Problem 2.
(a) What is the RMS average displacement of air particles for a pure-tone plane wave having a pressure of 0 dB-SPL at 1 kHz?
(b) Compare this to the thermal velocity of a nitrogen molecule. The thermal energy of a free air molecule is ET = (3/2)kT , where k = 1. 38 × 10 −^23 is Boltzmann’s constant. Thermal energy is a form of spread-spectrum kinetic energy, i.e., the molecule has an RMS thermal velocity vT (spread across all frequencies) of ET = (1/2)m|vT |^2 , where m is the mass of the nitrogen molecule. What is vT?
(c) Why is the thermal vibration of air molecules not audible?
Problem 2.
A person is speaking at an intensity of 66 dB-SPL, as measured with a sound level meter at 1 meter.
(a) Find the total power in the voice assuming that the level is uniform around the head.
(b) Find the total power assuming that the intensity varies as
I(θ, φ) = I 0 cos(θ/2) cos(φ/2) (1)
where θ is the angle in the horizontal plane, and φ in the vertical plane, relative to the “straight ahead” direction θ = 0, φ = 0.
Problem 2.
Problem Set 2 2
(a) How many millibels [mB] in 1 bel [B]? (b) Give the formula for the intensity in mB units.
(c) Give the formula for the sound pressure level in cB (centibel) units.
Problem 2.
Demonstrate that Pref ≡ 20 μPa is the same as Iref ≡ 10 −^12 [W/m^2 ].
Problem 2.
A bottle has a neck diameter of d = 1cm and is l = 1cm long. It is connected to the body of the bottle “barrel” which is D = 5cm in diameter and L = 10cm long. Treat the barrel as a short piece of transmission line, closed at one end, which looks like a compliance C = Vbarrel/ρ 0 c^2 , and the neck which look like a mass M = ρ 0 l/Aneck. These two impedances are in series, since they both see the same volume velocity (flow). Find the resonant frequency of the bottle.
Problem 2.
Sketch a cross-section of the vocal tract. Locate the lips, tongue tip, tongue body, epiglottis, glottis, pharynx, alveolar ridge, hard palate, velum (soft palate), and uvula.
Problem 2.
Suppose that a tube with characteristic impedance Z 0 [kg/m^4 s] is terminated in a cap whose acoustic impedance is ZL(s). Find the formula for the reflectance R(s) in terms of the load impedance ZL(s) and the characteristic impedance z 0 if:
(a) ZL(s) = R [kg/m^4 s]
(b) ZL(s) = 1/sC [kg/m^4 s]
(c) ZL(s) = r + sM [kg/m^4 s]
Problem 2.
Consider a two-tube model of the vocal tract, with two tubes of lengths L 1 = 8cm and L 2 = 9cm, with cross-sectional areas of A 1 = 1cm^2 and A 2 = 5cm^2. Assume that the terminating impedance at the lips is ZL = 0, and the terminating impedance at the glottis is ZG = ∞.
(a) The resonant frequencies of this system are those for which the sum of front and back cavity impedance is zero. Write an equation that, if solved, would tell you exactly the resonant frequencies of the front and back cavities.
