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Harmonics and Frequency Spectra in Sound Waves

Dive into the world of sound waves with this comprehensive guide on additive synthesis, harmonics, and fundamental frequencies. Learn how different harmonics combine to create complex sounds, explore frequency spectra, and understand the importance of fundamental frequencies. Discover the structure of waveforms and amplitude spectra, as well as the concept of critical bands and timbre in sound composition.

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Harmonics and Frequency Spectra in Sound Waves

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  1. Sound waves cont'd • Goldstein, pp. 331 – 339 • Cook, Chapter 7

  2. Additive synthesis • Fundamental frequency (or first harmonic): starting frequency for a complex sound • Harmonics: pure tones, each of which has a frequency that is a multiple of the fundamental

  3. Fundamental or first harmonic Frequency spectrum frequency: line's position amplitude: line's height Second harmonic Third harmonic

  4. Example • Fundamental or first harmonic: • 220 Hz, given amplitude • Third harmonic: • 660 Hz, 1/3 of amplitude • Fifth harmonic: • 1100 Hz, 1/5 of amplitude • Sum all of three:

  5. 12 harmonics • top down • bottom up

  6. Waveforms with 12 equal-amplitude sinusoids using cosine/Schroeder/random phase, at frequencies of 880, 440, 220, 110, 55, and 27.5 Hz

  7. Waveform and amplitude spectra. Periodic waveforms A through D have line spectra, the others either continuous spectra (E and F) or a band spectrum (G).

  8. Average spectral shape

  9. "Holy" spectra

  10. The width of critical bands as a function of center frequency

  11. Schematic representation of the frequency (heavy lines) corresponding to the tone sensation evoked by the superposition of two pure tones of nearby frequencies f1 and f2 = f1 +  f

  12. . All three instruments playing the note G3 with a fundamental frequency of 196 Hz.

  13. DemoMissing fundamental 300 Hz+ 600 Hz + 900 Hz + 1200 Hz 600 Hz + 900 Hz + 1200 Hz

  14. Sound composition and timbre: Helmholtz’s (1863) summary of the various subjective feelings pertaining onthe composition of a complex sound

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