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2.3 Consider two plane waves X, and X, traveling in the same direction. If they have the same frequency w but different amplitudes a; and phases 8;, then we can represent them by X, = a, cos (@t – S,) X = a, cos (@t– &) According to the principle of superposition, the resultant wave X is simply the sum of X, and X2. Show that X can be written in the form X= A cos (@t – $) where A? = a + a + 2a, a, cos(8, – 8,)

2.3 Consider two plane waves X, and X, traveling in the same direction. If they have the same frequency w but different amplitudes a; and phases 8;, then we can represent them by X, = a, cos (@t – S,) X = a, cos (@t– &) According to the principle of superposition, the resultant wave X is simply the sum of X, and X2. Show that X can be written in the form X= A cos (@t – $) where A? = a + a + 2a, a, cos(8, – 8,)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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2.3 Consider two plane waves X, and X, traveling in the same direction. If they have the same frequency w but different amplitudes a; and phases 8;, then we can represent them by X, = a, cos (@t – S,) X = a, cos (@t– &) According to the principle of superposition, the resultant wave X is simply the sum of X, and X2. Show that X can be written in the form X= A cos (@t – $) where A? = a + a + 2a,a, cos(&, – 8,)
Transcribed Image Text:2.3 Consider two plane waves X, and X, traveling in the same direction. If they have the same frequency w but different amplitudes a; and phases 8;, then we can represent them by X, = a, cos (@t – S,) X = a, cos (@t– &) According to the principle of superposition, the resultant wave X is simply the sum of X, and X2. Show that X can be written in the form X= A cos (@t – $) where A? = a + a + 2a,a, cos(&, – 8,)
and a, sin &, + a, sin ô, a, cos & + a, cos8, tan o
Transcribed Image Text:and a, sin &, + a, sin ô, a, cos & + a, cos8, tan o
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