Physics of Speech Notes

The Physics of Speech

Sounds as Symbols

• Symbol:

  • A form that represents something other than itself.

  • Words represent ideas, categories, entities.

• Phonemes:

  • Combinable elements that serve as the substance of the form of the word.

  • For spoken language, the signal that serves as the form half of the phoneme is sound.

Sounds as Segments

• Segment:

  • A unit of sound that is the manifestation of a phoneme.

  • A speech event of a certain time length, over which the acoustic signal is of a particular form and is relatively stable.

• Examples of segments:

  • sections of particular acoustic signals "thi s i s the b a d p l a ce"

Energy and Sound

• Sound:

  • A type of compression wave.

• Compression Wave:

  • Energy transmitted through some medium.

  • Fluctuations in density of the medium.

  • Radiating from a source.

  • Source =

• Examples of compression waves:

  • Ocean waves: density of water moves.

  • Sound: density of air moves. (perceivable as sound)

Energy and Sound: Sound Waves

• Sound waves are changes in air pressure over time.

• The size of air pressure difference represents loudness, also known as amplitude.

• The source for sound waves:

  • Some event that channels/directs energy in such a way as to affect air pressure

Waveforms

• Waveform:

  • A 2-dimensional plot of air pressure over time.

  • Examples include recordings of tuning forks and singing bowls, illustrated with plots.

• Pure tone:

  • A sound wave is a sinusoidal function.

  • Sine = ratio of 2 sides of a right triangle.

  • y = sin(x)

• sine = \frac{opp}{hyp}

Sound Waves

• Sound waves are periodic, meaning they have regular, repeated cycles.

• Period:

  • One full cycle of a wave.

• Frequency:

  • The rate of cycles.

  • Measured in Hertz (Hz), where 1 Hz = 1 cycle per second.

• Higher frequency means:

  • More cycles per unit of time.

  • Interpreted as a higher tone/pitch/note.

Sound Waves and Speech

• Speech sounds are not pure tones; they are regular (periodic) but complex.

• Energy source:

  • Vocal folds vibrating (like strings of an instrument).

  • Resonating in different ways in different chambers in the vocal tract.

Complex Waves in Speech

• Visual transformations of sound waves:

  • Complex waveforms can be represented via spectrograms

  • Spectrograms show the interplay of loudness × frequency × time.

  • They display glottal pulses (produced by the vocal folds) and their frequencies.

Acoustics of Speech Segments

• Different types of speech sounds:

  • Resonants, fricatives, stops.

  • Each is notable by its acoustic properties such as loudness, frequency, and turbulence.

Resonants

• Examples include vowels.

• They are combinations of resonant frequencies.

  • Harmonics: Overtones of a basic frequency.

  • Resonate or dampen in oral tract.

  • Resonant harmonics = formants.

  • Different formant combinations correspond to different vowels

Vowels

• Examples: i, e, a, o, u (ee, ay, oh, ooh)

• Vowel formant values for "i", "e", "a", "o", "u":

  • F1: "i" (low), "e" (mid), "a" (high), "o" (mid), "u" (low)

  • F2: "i" (high), "e" (mid), "a" (low)

Other Resonants

• Nasals (m, n) and liquids (l, r).

• Resonant like vowels, but not as loud

Fricatives

• Non-periodic sustained energy, producing turbulence.

• Different frequencies and loudness.

• Frequency: s > sh > f, th

Stops

• Characterized by silence.

• Stops affect the frequency of nearby sounds.

  • [p, b] pull formant frequency (F) down.

  • [t, d] pull F up.

  • [k, g] cause F to converge.

Sounds as Segments (Revisited)

• Segment: A speech event of a certain time length, over which the acoustic signal is of a particular form.

Sounds and Symbols

• Phonemes may present different acoustic forms in different contexts.

  • Example: k[ee]p ≠ p[ee]p (different acoustics, same phoneme /ee/).

  • [s]ue = [sh]e (same acoustics, different phoneme).

• Relationship:

  • word ↔ phonemes ↔ segments

  • The segment is a symbol: its form is acoustics, and the phoneme is the category it represents.