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The question is labelled W.24. The second picture shows the Three-Phase Miracle. Thanks!

example in Chapter 2 W.24 [See also W.25 and W.70.] Recollect the Three-Phase Miracle and construct an analogous four-phase miracle w.25 [See also W.24.] Recollect the Three-Phase Miracle example in Chapter 24, a construct an analogous five-phase miracle W.26 Two musicians simultaneously play what each hopes is high C (C5s frequency

EXAMPLE The Three-Phase Miracle] Three otherwise identical harmonic waves whose phases differ by 2 π/3 aka 120 ψ2R-A sin(k x-wt + 2 π/3) 3R A sin(k-wt +4 T/3) endure complete destructive interference when superposed: Though the medium may appear undisturbed, three distinct waves are present. PROOF of the Three-Phase Miracle The composite wave 23,I V2R +V3R İs readily determined from the two-wave superpo- sition analysis at the start of this chapter. The composite has the same wave number and angular frequency as the input waves. Its phase is equal to the ave phases, P23 (2n/3 + 4 π/3) π. Its amplitude is equal to twice the common input amplitude, multiplied by the cosine of one-half the phase difference between the input waves, viz., A23 2 A cos(T/3) A. Therefore, rage of the constituent 1R Thus, the superposition of all three waves cannot fail to vanish. ASIDE: Actually, this is not a miracle after all. Any set of [equally spaced] phases corresponding to complex roots of unity possesses this property.

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ー90。 4 그ゴ 2- ㄒㄧ Es 2 12

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