1. Harmonics and Spectra

(a) Complex waves can be mathematically analysed as being composed of different sine waves (Fourier analysis). Vibrating objects don't usually vibrate at a single frequency, they have harmonics.

(b) According to when each harmonic starts, the different elements of a complex wave can be in different phase relations (N.B. the human ear is not thought to be sensitive to phase relations).

(c) Very important: any complex wave can be analysed into the periodic elements of different frequencies of which it is composed. Result: the spectrum of sound. For example, the following spectrum is of the waveform produced at the glottis in a vowel. Note the series of peaks or harmonics, occurring at integer multiples of the fundamental frequency f₀.
 

107dB 5500Hz Fig. 1

(Click on the graph to hear an imitation of the sound that comes out of the larynx.)

(d) Non-periodic sounds are more adequately represented not by line spectra but by a continuous spectrum.

 

100dB 8000Hz

100dB 8000Hz

(a) Natural frequencies and resonance - different objects more or less tuned to specific frequencies - can act as filters.

Filters have centre frequency and bandwidth - the range of frequencies passed by filter not more than 3dB down on its maximum amplitude. The bandwidth of a filter may be relatively narrow or broad.
 

3. Source + Filter theory: Vowel Sounds

(a) The vocal tract acts as a complex variable filter. Into this is input a signal from the glottal source (for voiced sounds). Fig 1 shows a glottal source wave for a vowel, i.e. a complex wave with numerous harmonics which rapidly decrease in amplitude as frequency increases (12 dB/octave).

(b) Vowel sounds seen as product of glottal source and variable filtering effect of supraglottal tract. So, the same vowels have the same gross spectral shape, irrespective of the fundamental frequency f₀ of the source.
 
 

Fig. 1 filtered once ...

filtered twice ...

and filtered 3 times