A phasor diagram shows two arrows of equal length units

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

Optics and Photonics, Ch Harmonic waves, phasors and group velocity

Problem

A phasor diagram shows two arrows of equal length 4.004.00 units, both rotating together at ω=5.00×108 rad s−1\omega = 5.00\times10^{8}\ \mathrm{rad\,s^{-1}}; the second arrow is drawn 90.0∘90.0^\circ ahead of the first, measured anticlockwise. Under convention CV3 an arrow at anticlockwise angle ϕ\phi from the reference direction represents, at a fixed point, the wave E0cos⁡(ωt−ϕ)E_0\cos(\omega t-\phi). ((a)) Write down the two waves the arrows represent, E1(t)E_1(t) and E2(t)E_2(t), taking the first arrow's phase as zero. ((b)) Add the two phasors, using the cosine rule and tangent rule for the resultant of two arrows, to find the single arrow that represents their sum, and write the result as one cosine wave E(t)=E0cos⁡(ωt−ϕ)E(t)=E_0\cos(\omega t-\phi).

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