Harmonics Review Music to my ears?. Standing Waves Vibrating Strings Each standing wave has a different frequency Single pitches = Multiple frequencies.

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Presentation transcript:

Harmonics Review Music to my ears?

Standing Waves Vibrating Strings Each standing wave has a different frequency Single pitches = Multiple frequencies Nodes Antinodes Wavelength ~ λ 1 = 2L V = f λ f = V/ λ

Standing Waves Fundamental Frequency f 1 = V/ λ 1 or V/2L Lowest possible frequency of a standing wave

Harmonics Multiples of the fundamental frequency f 2 = 2 f 1 Wavelength is half = frequency that is twice as much

Harmonic Series First Harmonic λ 1 =2Lf1f1 2 nodes 1 antinode Second Harmonic λ 2 = L f 2 = 2f 1 3 nodes 2 antinodes Third Harmonic λ 3 = (2/3) L f 3 =3f 1 4 nodes 3 antinodes Fourth Harmonic λ 4 = (1/2) L f 4 =4f 1 5 nodes 4 antinodes

Harmonic Series f n = n (V/2L) Frequency = harmonic # (speed of wave)___ 2 (length of string)