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Chrome File Edit View History Bookmarks Window People Help 40% Thu 53 AM QA E Wiz Khalifa Remember x y WA GRADED Assignment 7 x C Light Polarized In The X D motor 1.physics.wayne.edu x C chegg study l Guided sol www.webassign.net/web/Student/Assignment-Responses/submit?dep 10627919 EE App Lab board Learn w WSU Pipeline Log smartwork version 3 WA WebAssign LOG IN E Soccer News and Sc YouTube CHASE Bank credi C Home I Chegg.com negative y direction positive or negative z direction o -20 points GRRPhys2 22.TB.037 My Notes o Ask Your Teacher In vacuum, the components of an EM wave are E 50 (V/m)cos[(5.00 m 1)x at], E 0, and E 0. What is w? 1.50 x 109 rad/s 1.20 x 109 rad/s 1.00 x 109 rad/s 8.00 x 108 rad/s more information is needed Submit Answer Save Progress My Notes o Ask Your Teacher 3. C 20/20 points I Previous Answers GRRPhys2 22.TB.046 Alum2. electric field? tencitv n

Explanation / Answer

You can figure it out by requiring that Ey at x have the same value as Ey at x+L, where "L" is one wavelength;

(50)Cos(5x + wt) = (50)Cos(5x + 5L + wt)

Now this can be done for any time "t" but it is a little easier to choose t=0: Then, canceling the "50" the requirement isCos(5x) = Cos(5x+5L)

Now use the "double angle" trig identity on the right side term;

Cos(5x) = Cos(5x)Cos(5L) - Sin(5x)Sin(5L)

By inspection, this equality will hold if, 5L = 2(pi)
Thus;
L = 2(pi)/5 = (.4)pi

ANOTHER METHOD is to simply know the general format for any traveling wave of wavelength "L" and frequency "w" is

F(x,t) = ACos(2pix/L + wt)

often written as;

F(x,t) = ACos(kx + wt), where k= 2pi/L

Then you can get your answer by comparing your given "(50)Cos(5x + wt) with the general format and see that;

5 = 2pi/L
L = 2pi/5.

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