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superposition

Simply add the effect of each wave at every moment. Green + Blue = Red. superposition. pressure or displacement. time (ms). The resultant frequency is the Greatest Common Factor of the component frequencies: f new = GCF( f 1 , f 2 ). Beating. f 1 = 5 f 2 = 5.5 f comb = .5.

lillian-gilliam
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superposition

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  1. Simply add the effect of each wave at every moment Green + Blue = Red superposition pressure or displacement time (ms) The resultant frequency is the Greatest Common Factor of the component frequencies:fnew = GCF(f1,f2)

  2. Beating f1= 5 f2= 5.5 fcomb= .5 f1= 20 f2= 21 fcomb= 1 The beat frequency is the difference of the component frequencies f1= 500 f2= 501 f1= 500 f2= 505 f1= 500 f2= 510

  3. Harmonics What is the greatest common factor of... (10, 20, 30, 40, ...)? (150, 300, 450, 600, ...)? (440, 880, 1320, 1760, ...)? perceived pitch is always the fundamental frequency f1 fundamental 2nd harmonic f2 = 2 f1 3rd harmonic f3 = 3 f1 4th harmonic f4 = 4 f1

  4. Superposition of many harmonicssawtooth wave f +2f (A2 = 1/2) f =500 Hz (A = 1) f +2f +3f (A3 = 1/3) f +2f +3f+4f+5f (A5 = 1/5) 10 harmonics

  5. Superposition of many sine wavessquare wave f =500 Hz (A = 1) f +3f (A3 = 1/3) f +3f+5f (A5 = 1/5) f +3f+5f+7f+9f (A9 = 1/9) 10 harmonics

  6. A sound is the sum of its parts Piano Fundamental only Harmonics 1 & 2 Harmonics 1, 2, 3 Harmonics 1-4 Harmonics 1-5 Harmonics 1-6 Full sound

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