At a fixed point on a beam

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

At a fixed point on a beam, two harmonic waves of the same frequency are represented by two phasors (arrows) drawn from a common origin. The first arrow has length

E_1 = 5.0\ \mathrm{V\,m^{-1}}

and lies along the reference direction (angle

0

). The second has length

E_2 = 12.0\ \mathrm{V\,m^{-1}}

and is turned by

\delta = 90^\circ

from the first, in the sense of increasing phase constant. Both arrows turn together at the angular frequency

\omega

, so the angle between them is fixed. Translate the diagram into an equation: write the resultant as

E = E_0\cos(kx - \omega t + \phi)

and find ((a)) the resultant amplitude

E_0

; ((b)) the phase constant

\phi

of the resultant, in degrees, measured from the first arrow.

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