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Voice and vowel acoustics: source-filter theory, harmonics, formants and the spectrogram
Voice is created at a source (the vocal folds, giving F0 and harmonics) and shaped by a filter (the oral and pharyngeal cavities, giving formants). The two parts are nearly independent: changing pitch changes the spacing of the harmonics, and changing mouth shape changes the formants.
Why it matters in the exam
The bank asks short calculations: F0 = 1 over the period (a 5 ms period — 200 Hz), and harmonic number n sits at n times F0 (the third — 600 Hz). The number of semitones between two frequencies is 12 times log2 of their ratio (from 110 to 440 Hz — 24). The vocal tract behaves like a tube shut at the vocal folds and open at the mouth: Fn = (2n-1) × c ÷ 4L, and for a 17.5 cm tube (c = 350) the formants are 500, 1500 and 2500 Hz. Lengthening the tube (rounding and protruding the lips) lowers every formant; in a child the tube is short and the formants high, and listeners normalise them for the talker.
Reading vowels: F1 runs opposite to tongue height (a high vowel — low F1), and F2 rises as the tongue moves forward; F1 near 300 and F2 near 2300 Hz in a man is /i/. The vowel /a/ is louder than /i/ because its F1 is high. In a teenager with congenital deafness the vowel space shrinks toward the centre (F2 of /i/ falls and that of /u/ rises). Nasality adds resonance and anti-resonance pairs, mostly around F1, and F1 grows weaker. A wideband spectrogram (about 300 Hz) shows formants and vertical striations — each striation is one vocal-fold pulse; a narrowband one (about 45 Hz) separates the harmonics. In breathy voice the first harmonic is strong relative to the second and high harmonics are weak; in pressed voice the spectrum is flatter. Stress in Hebrew is marked mainly by duration and F0, and a yes/no question by a final F0 rise.
Key points
- Source: F0 and harmonics at whole-number multiples; filter: formants.
- Closed-open tube: 500, 1500, 2500 Hz for 17.5 cm.
- F1 — height (inverse), F2 — frontness; rounding lowers formants.
- Wideband for formants and timing, narrowband for harmonics.
- Semitones = 12 × log2 of the ratio.
Summary table
| Concept | Definition or formula | Example |
|---|---|---|
| F0 and harmonics | F0 = 1 ÷ T; harmonics at whole-number multiples | A 5 ms period: F0 of 200, third harmonic 600 |
| Semitones | 12 × log2(f2 ÷ f1) | 110 to 440 Hz = 24 semitones (2 octaves) |
| Tube model | Fn = (2n-1) × c ÷ 4L | 17.5 cm: 500, 1500, 2500 Hz; a longer tube — all fall |
| F1 and F2 | F1 — tongue height (inverse); F2 — frontness | /i/: low F1, high F2; /a/: high F1 |
| Nasality | Extra resonance and anti-resonance; weak, wide F1 | Expected in cleft palate with hypernasality |
| Spectrogram | Wideband — formants and vertical striations; narrowband — harmonics | F0 of 100: a striation every 10 ms |
| Voice quality and prosody | Breathy: strong H1, steep tilt; pressed: flatter | A Hebrew question: a final F0 rise |
A free exam question
In an acoustic analysis of vowels in a child with cleft palate and hypernasality, which finding is expected?
- A. Higher F1 amplitude and a narrower F1 bandwidth in all vowels
- B. A rise in F0 of about one octave in every vowel produced
- C. Lower F1 amplitude and wider bandwidth, plus nasal resonances
- D. A short noise burst at the onset of every vowel
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Sources
- Fant, Acoustic Theory of Speech Production, 1960 — Source-filter theory
- Kent & Read, The Acoustic Analysis of Speech, 2nd edition (2002) — Vowels; spectrography
- Raphael, Borden & Harris, Speech Science Primer, 6th edition (2011) — Acoustics of speech production
Sources are given for further reading; the text is written afresh and not copied from them.
Reviewed by the Examqo AI Professor · 2026-11-02. The text may contain errors; when in doubt, check the source.