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Harmonics

Harmonics. Physics Chapter 13-3 Pages 494-503. A. Standing waves on a vibrating string. Fundamental frequency – lowest frequency of vibration of a standing wave  Symbolized as f 1 Harmonic series – series of frequencies which are multiples of the fundamental frequency

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Harmonics

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  1. Harmonics Physics Chapter 13-3 Pages 494-503

  2. A. Standing waves on a vibrating string Fundamental frequency – lowest frequency of vibration of a standing wave  Symbolized as f1 Harmonic series – series of frequencies which are multiples of the fundamental frequency  f2, f3, f4, …

  3. Equation v = fλ f = v / λ Fundamental frequency of a string fixed at both ends  f1 = v/λ1 = v/2L L = string length

  4. Harmonics(multiples of f1) FrequencyWavelength f2 = 2 f1 λ2 = L f3 = 3 f1 λ3 = 2/3 L f4 = 4 f1 λ4 = ½ L

  5. Harmonic Series of standing waves on vibrating string fn = n (v/2L) n = 1, 2, 3, … n = harmonic # v = speed of the waves on a string L = string length f = frequency

  6. * If you put a finger down on a string, now only part is vibrating and a new fundamental frequency is created - Many fundamental frequencies can be produced on a single string - Table 13-3 page 495

  7. B. Standing waves in a column of air • Standing waves can be set up in a tube of air  examples: organ pipes, trumpet, flute Some move down the tube, some reflect back up forming a standing wave

  8. Harmonic series of a pipe open at both ends fn = n (v/2L) n = 1, 2, 3, … **All harmonics possible Open ends are antinodes and allow free range of motion (*different than a string) Can change f1 by making the column of air longer or shorter Simplest standing wave in pipe = ½ λ (length of the pipe)

  9. Harmonic series of a pipe closed at one end Examples: trumpet, saxophone, clarinet - the shape of the instrument will affect the harmonics Movement of air is restricted at closed end creating a node - Open end is an antinode - Only the odd harmonics are possible - Simplest standing wave = ¼ λ fn = n (v/4L) n = 1, 3, 5, … ** Pitch determine by the fundamental frequency ** 2nd harmonic is 1 octave above the fundamental frequency

  10. C. Timbre (sound quality) - Quality of a steady musical sound - Different mixtures of harmonics produce different sound quality - Instruments have a characteristic timbre

  11. D. Beats – interference of waves of slightly different frequencies traveling in the same direction • Appears as a variation in loudness from soft to loud to soft • Waves combine due to superposition Constructive (in phase) and destructive (out of phase) interference • Beats per second corresponds to differences in frequency between the waves / sounds

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