Three harmonic waves of the same frequency arrive at one point of a screen and superpose

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

Three harmonic waves of the same frequency arrive at one point of a screen and superpose. Written with the convention of this book they are E1=6.0cos⁡(kx−ωt),E_1 = 6.0\cos(kx - \omega t),E2=4.0cos⁡(kx−ωt+90∘),E_2 = 4.0\cos(kx - \omega t + 90^\circ),E3=3.0cos⁡(kx−ωt+180∘),E_3 = 3.0\cos(kx - \omega t + 180^\circ), with all amplitudes in V m−1\mathrm{V\,m^{-1}}. ((a)) Draw the three phasors from a common origin and add them head to tail; state the horizontal and vertical components of the resultant arrow. ((b)) Hence give the resultant amplitude E0E_0 and its phase constant ϕ\phi in degrees, and write the resultant as a single harmonic wave.

Browse the problem library