{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

tutorial15Solution

# tutorial15Solution - The University of Western Australia...

This preview shows pages 1–2. Sign up to view the full content.

The University of Western Australia School of Electrical, Electronic and Computer Engineering Solutions - Tutorial Sheet 15, 2006 Electromagnetic Theory ENGT3303 Question 1 The resulting plane wave is obtained by superposition and is given by ( ) ( ) ( ) z t A z t A t z 2 2 1 1 cos cos , β ω β ω + = Ψ If we substitute in the four equations for ω 1 , ω 2 , β 1 , and β 2 , as given in the question and use the identity ( ) β α β α β α sin sin cos cos cos m = ± , the resultant wave becomes ( ) ( ) ( ) z t z t A t z β ω β ω = Ψ cos cos 2 , This resultant wave is a carrier wave at frequency ω = ω 1 + ω 2 ( ) /2 and phase velocity v = ω / β . The amplitude of the carrier wave is a wave of frequency ω , called the beat frequency, and propagation constant β traveling at velocity v g = ∆ ω / β . time group carrier This velocity is called the group velocity, and represents the rate of flow of energy. This simple argument can be extended to n waves, whereupon, the “group” nature becomes more apparent.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern