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 μ, and three heavy objects, each of mass M = 2.35 kg, as shown in the figure. L1 M 12 42 L3 M La 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 L₁ = 35.0 cm having a frequency of middle C in the equal-tempered scale, f₁ = 261.6 Hz. In the just scale, musical intervals between two notes are defined by frequencies of the notes whose ratios 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 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 fc = 5. The third note in the 4 fG_3 C-G interval is= Before embarking on building the system, you need to determine what the lengths of the other two fc 2 wires should be (in cm). cm cm
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 μ, and three heavy objects, each of mass M = 2.35 kg, as shown in the figure. L1 M 12 42 L3 M La 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 L₁ = 35.0 cm having a frequency of middle C in the equal-tempered scale, f₁ = 261.6 Hz. In the just scale, musical intervals between two notes are defined by frequencies of the notes whose ratios 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 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 fc = 5. The third note in the 4 fG_3 C-G interval is= Before embarking on building the system, you need to determine what the lengths of the other two fc 2 wires should be (in cm). cm cm
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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 linear mass density μ, and three heavy objects, each of mass M = 2.35 kg, as shown in the figure.
L₁
42
L3
M
L2
M
La
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 L₁ = 35.0 cm having a frequency of
middle C in the equal-tempered scale, f₁ = 261.6 Hz. In the just scale, musical intervals between two notes are defined by
frequencies of the notes whose ratios are those of small whole numbers. In a C major chord, the first note in the chord is C
fE 5
The third note in the
fc 4
and the second note is E. In the just scale, the ratio of the frequencies in the C-E interval is
=
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
fG_3
C-G interval is = Before embarking on building the system, you need to determine what the lengths of the other two
fc 2
wires should be (in cm).
cm
cm
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