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After reading the chapter on superposition and standing waves, you decide to design a special wind chime. It consists of three light wires, of
After reading the chapter on superposition and standing waves, you decide to design a special wind chime. It consists of three light wires, of linear mass density, and three heavy objects, each of mass M = 2.20 kg, as shown in the figure. L M La M Ls M The entire system is suspended from the ceiling. When the wind blows, it sets all three wires into vibration. You want the system to play a C major chord in the just scale, with the upper wire of length L = 46.0 cm having a frequency of middle C in the equal-tempered scale, f = 261.6 Hz. In the just scale, musical intervals between two notes are defined by frequencies of the notes whose ratios = The third are those of small whole numbers. In a C major chord, the first note in the chord is C and the second note is E. In the just scale, the ratio of the frequencies in the C-E interval is note in the C major chord is G, so the chord also contains a C-G interval. In the just scale, the ratio of the frequencies in the C-G interval is need to determine what the lengths of the other two wires should be (in cm). fG 3 fc Before embarking on building the system, you 5 4 fc 2 L2 cm L3 cm
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