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Exercise. 9 Considering Section 7.1, suppose we began the analysis to find E = E¡ + E2 with two cosine functions E1 = E01 cos (@t + aj) and E2 = E02 cos (wt + a2). To make things a little less complicated, let E01 = E02 and j = 0. Add the two waves algebraically and make use of the familiar trigonometric identity cos 0 + cos Þ = 2 cos}(0 + 4) cos (0 – 4) in order to show that E = Eo cos (wt + a), where Eo = 2E01 cos a2/2 and a = a2/2. Now show that these same results follow from Eqs. (7.9) and (7.10). %3D E = Eổi + Eổ2 + 2E01E02 cos (a2 – a1) (7.9) %3D That's the sought-after expression for the amplitude (Fo) of the esultant wave. Now to get the phase, divide Eq. (7.8) by (7.7): E01 sin æj + E02 sin a2 tan a (7.10) Eo1 cos a¡ + E02 cos a2

Exercise. 9 Considering Section 7.1, suppose we began the analysis to find E = E¡ + E2 with two cosine functions E1 = E01 cos (@t + aj) and E2 = E02 cos (wt + a2). To make things a little less complicated, let E01 = E02 and j = 0. Add the two waves algebraically and make use of the familiar trigonometric identity cos 0 + cos Þ = 2 cos}(0 + 4) cos (0 – 4) in order to show that E = Eo cos (wt + a), where Eo = 2E01 cos a2/2 and a = a2/2. Now show that these same results follow from Eqs. (7.9) and (7.10). %3D E = Eổi + Eổ2 + 2E01E02 cos (a2 – a1) (7.9) %3D That's the sought-after expression for the amplitude (Fo) of the esultant wave. Now to get the phase, divide Eq. (7.8) by (7.7): E01 sin æj + E02 sin a2 tan a (7.10) Eo1 cos a¡ + E02 cos a2

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Exercise. 9 Considering Section 7.1, suppose we began the analysis to find E = Ej + E2 with two cosine functions E1 = E01 cos (@t + aj) and E2 = E02 cos (wt + a2). To make things a little less complicated, let E01 = E02 and j = 0. Add the two waves algebraically and make use of the familiar trigonometric identity cos 0 + cos = 2 cos} (0 + 4) cos (0 – 4) in order to show that E = Eo cos (wt + a), where Eg = 2E01 cos a2/2 and a = a2/2. Now show that these same results follow from Eqs. (7.9) and (7.10). E = Eổi + Eổa + 2E01E02 cos (a2 – a1) (7.9) That's the sought-after expression for the amplitude (Fo) of the esultant wave. Now to get the phase, divide Eq. (7.8) by (7.7): E01 sin aj + E02 sin a2 tan a = (7.10) E01 cos aj + E02 cos a2
Transcribed Image Text:Exercise. 9 Considering Section 7.1, suppose we began the analysis to find E = Ej + E2 with two cosine functions E1 = E01 cos (@t + aj) and E2 = E02 cos (wt + a2). To make things a little less complicated, let E01 = E02 and j = 0. Add the two waves algebraically and make use of the familiar trigonometric identity cos 0 + cos = 2 cos} (0 + 4) cos (0 – 4) in order to show that E = Eo cos (wt + a), where Eg = 2E01 cos a2/2 and a = a2/2. Now show that these same results follow from Eqs. (7.9) and (7.10). E = Eổi + Eổa + 2E01E02 cos (a2 – a1) (7.9) That's the sought-after expression for the amplitude (Fo) of the esultant wave. Now to get the phase, divide Eq. (7.8) by (7.7): E01 sin aj + E02 sin a2 tan a = (7.10) E01 cos aj + E02 cos a2
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