sum_lecture11 - T he Physics of L ight Sound Mersennes Laws...

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The Physics of Light & Sound Mersenne’s Laws & Longitudinal Standing Waves Drs. Paulson and Scully GSCI 121 Summer 2011
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Standing Waves Standing waves are characterized by nodes and antinodes . Nodes are areas where destructive interference takes place while antinodes are places where constructive interference is taking place. N N N N N N N AN AN AN AN AN AN AN AN
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A fundamental frequency of a wave on a string is one antinode with nodes at the ends. We can fit integer, N, ½ wavelengths on the string. These are known as harmonics or overtones . Overtones Fundamental or 1 st Harmonic 2 nd Harmonic 3 rd Harmonic 4 th Harmonic
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Suppose that a string fixed at both ends has a length, L. For the first harmonic, ½ λ = L. And since c = λf: Overtones Harmonic Wavelength λ Frequency (f = v/ ) λ 1 λ 1 = 2L f 1 = c/ (2L) 2 λ 2 = L = ½ λ 1 f 2 = c/L = 2 f 1 3 λ 3 = L = ⅓ λ 1 f 3 = c/( L) = 3 f 1 4 λ 4 = ½ L = ¼ λ 1 f 4 = c/(½ L) = 4 f 1 5 λ 5 = L = ⅕ λ 1 f 5 = c/( L) = 5 f 1 6 λ 6 = L = ⅙ λ 1 f 6 = c/( L) = 6 f 1 f 1 = c 2 L
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