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## Main Question or Discussion Point

I am confused with this part of "Introduction to Electrodynamics" 3rd edition by Dave Griffiths.

On page 367, the travelling wave is represented by:

[tex] f(z,t)\;=\; A cos[k(z-vt) \;+\; \delta] [/tex] 9.7

Where v is velocity and [itex]kv=\omega[/itex]. This give:

[tex] f(z,t)\;=\; A cos[kz \;-\;\omega t \;+\; \delta] \;\hbox { for forward moving wave and }[/tex] 9.12

[tex] f(z,t)\;=\; A cos[kz \;+\;\omega t \;-\; \delta] \;\hbox { for backward moving wave and }[/tex] 9.13

[tex]f(z,t) \;=\; Re[A e^{i(kz-\omega t + \delta)} ] \;\hbox { and }[/tex] 9.16

[tex]\tilde{f}(z,t) \;=\; \tilde{A}e^{i(kz-\omega t )}[/tex] 9.17

I have no problem with 9.16 because the real part is cosine and it is an even function. The convension way is always written like:

[tex]f(z,t) \;=\; Re[A e^{i(\omega t \;-\;kz \;+\; \delta)}][/tex]

I have issue with 9.17 because this is not just the real part.

[tex] e^{i (kz-\omega t) } = cos (kz\;-\;\omega t) \;+\; i sin (kz\;-\;\omega t) \;\hbox { which is not the same as } \;e^{i (\omega t \;-\; kz) } \;=\; cos (\omega t \;-\; kz) \;+\; i sin (\omega t \;-\;kz) [/tex]

The sine portion has opposite sign.

Then on P384 section 9.3.2 , the book give the equation of the incident electric wave and reflected electric wave :

[tex] \tilde { E} _I(z,t) \;=\; \hat x \tilde {E}_{0_I} e^{i(kz-\omega t)} \;\hbox { and }[/tex] 9.75

[tex] \tilde { E} _R(z,t) \;=\; \hat x \tilde {E}_{0_R} e^{i(-kz-\omega t)} [/tex] 9.76

I have issue with 9.76 because this is not just the real part.

[tex] e^{i (-kz-\omega t) } = cos (kz\;+\;\omega t) \;-\; i sin (kz\;+\;\omega t) \;\hbox { which is not the same as } \;e^{i (kz\;+\;\omega t) } \;=\; cos (kz\;+\;\omega t) \;+\; i sin (kz\;+\;\omega t) [/tex]

Something is wrong on the equation of the reflected wave. But This book have no error that I can find so far, so what did I do wrong? Please help.

Thanks

Alan

On page 367, the travelling wave is represented by:

[tex] f(z,t)\;=\; A cos[k(z-vt) \;+\; \delta] [/tex] 9.7

Where v is velocity and [itex]kv=\omega[/itex]. This give:

[tex] f(z,t)\;=\; A cos[kz \;-\;\omega t \;+\; \delta] \;\hbox { for forward moving wave and }[/tex] 9.12

[tex] f(z,t)\;=\; A cos[kz \;+\;\omega t \;-\; \delta] \;\hbox { for backward moving wave and }[/tex] 9.13

[tex]f(z,t) \;=\; Re[A e^{i(kz-\omega t + \delta)} ] \;\hbox { and }[/tex] 9.16

[tex]\tilde{f}(z,t) \;=\; \tilde{A}e^{i(kz-\omega t )}[/tex] 9.17

I have no problem with 9.16 because the real part is cosine and it is an even function. The convension way is always written like:

[tex]f(z,t) \;=\; Re[A e^{i(\omega t \;-\;kz \;+\; \delta)}][/tex]

I have issue with 9.17 because this is not just the real part.

[tex] e^{i (kz-\omega t) } = cos (kz\;-\;\omega t) \;+\; i sin (kz\;-\;\omega t) \;\hbox { which is not the same as } \;e^{i (\omega t \;-\; kz) } \;=\; cos (\omega t \;-\; kz) \;+\; i sin (\omega t \;-\;kz) [/tex]

The sine portion has opposite sign.

Then on P384 section 9.3.2 , the book give the equation of the incident electric wave and reflected electric wave :

[tex] \tilde { E} _I(z,t) \;=\; \hat x \tilde {E}_{0_I} e^{i(kz-\omega t)} \;\hbox { and }[/tex] 9.75

[tex] \tilde { E} _R(z,t) \;=\; \hat x \tilde {E}_{0_R} e^{i(-kz-\omega t)} [/tex] 9.76

I have issue with 9.76 because this is not just the real part.

[tex] e^{i (-kz-\omega t) } = cos (kz\;+\;\omega t) \;-\; i sin (kz\;+\;\omega t) \;\hbox { which is not the same as } \;e^{i (kz\;+\;\omega t) } \;=\; cos (kz\;+\;\omega t) \;+\; i sin (kz\;+\;\omega t) [/tex]

Something is wrong on the equation of the reflected wave. But This book have no error that I can find so far, so what did I do wrong? Please help.

Thanks

Alan