Acoustic and Auditory Phonetics Chapter 2 part 2

Transcription

1 Acoustic and Auditory Phonetics Chapter 2 part 2 Jeffrey Heinz heinz@udel.edu University of Delaware February 19, /24

2 Source-Filter Theory of Speech 2/24

3 Modeling the schwa Last week we modeled the vocal tract as a uniform tube closed at one end (the glottis) and open at the other (the lips). The first three formants of [@] for a tube 17.5cm long F1 = 500Hz F2 = 1500Hz F3 = 2500Hz For shorter vocal tracts, (e.g. 15cm) the formant frequencies increase. 3/24

4 Resonance Objects resonate at their own particular frequencies. 1. This is how sopranos are said to be able to break a glass by singing at the right pitch. 2. It s also the idea behind how you can swing yourself higher on a swing by pumping at just the right time. 3. It s like positive feedback. 4/24

5 Resonances in Tubes 1. Columns of air within a tube also have resonances (called formants when speaking of the vocal tract). 2. As sound is passed through a tube, frequencies which match the resonant frequencies are enhanced whereas those which do not match are damped. 5/24

6 Source-Filter Theory Source of speech sounds The speech source is a complex sawtooth-shaped wave, which is the sum of many simple waves with different frequencies. 6/24

7 Source-Filter Theory Spectrum of the source The spectrum of this sawtooth-waved reveals it is the sum of multiple simple waves. The peaks in the spectrum are called harmonics. 7/24

8 Source-Filter Theory Spectrum of the filterered source Here we see the spectrum of this sound after it has been filtered. 8/24

9 Calculating resonant frequencies 1. Tube closed at both ends f k = kc 2L 2. Tube closed at one end and open at the other (resembles the vocal tract) (2k 1)c f k = (2) 4L L = length of tube, c = speed of sound, k is a positive integer These resonant frequencies f k are called the kth formant frequencies. (1) 9/24

10 Uniform tube open at one end is like Formants are resonant frequencies of the vocal tract 1. Approximate length of average male s vocal tract L=17.5cm 1.1 The first formant is 35,000/70 = 500Hz 1.2 The second formant is /70 = = 1500 Hz 1.3 The third formant is /70 = = 2500 Hz 2. Approximate length of average female s vocal tract L = 15cm 2.1 The first formant is 2.2 The second formant is 2.3 The third formant is 10/24

11 Uniform tube open at one end is like Formants are resonant frequencies of the vocal tract 1. Approximate length of average male s vocal tract L=17.5cm 1.1 The first formant is 35,000/70 = 500Hz 1.2 The second formant is /70 = = 1500 Hz 1.3 The third formant is /70 = = 2500 Hz 2. Approximate length of average female s vocal tract L = 15cm 2.1 The first formant is 35,000/60 = 583.3Hz 2.2 The second formant is /60 = = 1750 Hz 2.3 The third formant is /60 = = 2917 Hz 10/24

12 A little more physics These vibrating columns of air which resonate are a property of standing longitudinal waves. 11/24

13 Resonance in tubes closed at both ends Recall what happens when the compression is sent down the length of the tube closed at both ends: It bounces back, canceling out the area of rarefaction that is following it. 12/24

14 Standing Waves in Tubes Closed at both ends The standing wave pattern of the 1st resonance in a tube closed from both ends (Figure 5.8 from Johnson (2004)). The nodes are places where the waves constantly out of sync, leaving the pressure exactly neutral. The antinodes are places where the waves are constantly in sync, creating maximal areas of compression and rarefaction. 13/24

15 Standing Waves in Tubes Closed at both ends The standing wave pattern of the 2nd resonance in a tube closed from both ends (Figure 5.8 from Johnson (2004)). The nodes are places where the waves constantly out of sync, leaving the pressure exactly neutral. The antinodes are places where the waves are constantly in sync, creating maximal areas of compression and rarefaction. 13/24

16 Demo: Nodes and Antinodes /24

17 Standing Waves in Tubes Closed at One End and Open at the Other The standing wave pattern of the 1st resonance in a tube closed at one end, open at the other (Figure 5.9 from Johnson (2004)). 15/24

18 Standing Waves in Tubes Closed at One End and Open at the Other The standing wave pattern of the 2nd resonance in a tube closed at one end, open at the other (Figure 5.9 from Johnson (2004)). 15/24

19 One more technical consideration Pressure vs. velocity 1. Standing waves can also be described in terms of particle displacement, i.e. velocity. 2. The nodes of one kind are the antinodes of the other and vice versa. 16/24

20 Velocity Standing Waved Demo 17/24

21 Why we care The vocal tract is clearly nothing like a uniform tube most of the time. Recall that in source-filter theory the vocal tract acts as a filter and resonator on the glottal source. Figure: Vocal tract configurations and filters (from Ladefoged 1996) How can we predict which vocal tract shapes will have which resonances? 18/24

22 Preview of what s coming after Spring Break 1. In the second part of this course, we will look at two ways to predict the resonances of nonuniform tubes: 1.1 Multitube models, which treat the nonuniform vocal tract as if it were a concatenation of small tube-like sections. 1.2 Pertubation theory, which lets us determine how formants deviate from the norm if there are constrictions near the nodes or antinodes of the standing wave patterns (which recall are a result of the resonant frequencies) 19/24

23 Illustration of Main Idea in Quantal Theory (From Stevens 1998) Articulatory space is necessarily continuous, but slightly different articulations can produce qualitatively different acoustic effects, especially in region II. 20/24

24 Illustration of Main Idea in Quantal Theory (From Stevens 1998) There is a large acoustic (and auditory) difference between regions I and III. 20/24

25 Illustration of Main Idea in Quantal Theory (From Stevens 1998) Within regions I and III, however, the acoustic parameter is relatively insensitive to change in the articulatory parameter. In other words, changes in articulation don t have much effect on the speech output. 20/24

26 Illustration of Main Idea in Quantal Theory (From Stevens 1998) Stevens claim is that linguistic contrasts involve differences between quantal regions; i.e. regions of acoustic stability (I and III). 20/24

27 Quantal Theory (Stevens 1972, 1989) 1. Articulations don t have to be precise to produce a certain output. 2. Continuous movement through a quantal region will yield an acoustic steady state. 21/24

28 Quantal Theory (Stevens 1972, 1989) 1. Strong Hypothesis of Quantal Theory: All quantal regions (I and III) define contrastive sounds and all contrastive sounds differ quantally. 21/24

29 Predictions of Quantal Theory i u a These three vowels are preferred cross-linguistically, so they should be quantal vowels. Later we will see that in fact they are. 22/24

30 Why do quantal regions influence sound systems? 1. Speakers can get away with articulatory sloppiness if languages make use of quantal phonetic categories. 2. Near-continuous articulations yield discrete acoustic (perceptual) categories. 23/24

31 Summary 1. Vibrating air within tubes resonate at certain frequencies. 2. We can calculate the resonant frequencies if we know the the length of the tube, the speed of sound, and which resonant frequency we want (the first, second or third etc.) 3. These resonances also create standing wave patterns with nodes and antinodes. 4. The physics we have studied here provides the basis for the acoustic analysis of speech sounds, which we will return to after spring break. Quantal theory explores the hypothesis that speech sounds occur in regions of acoutic stability. 24/24