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Two parallel traveling plane waves have different angular frequencies w₁ and w2 and pressure amplitudes P₁ and P₂. (a) Show that the instantaneous energy density &; at a point in space varies between (P₁ + P₂)² / poc² and (P₁ – P₂)² / poc². (b) Show that the total energy density at the point averages to the sum of the individual energy densities of each wave alone. Hint: Let the averaging time be much greater than 2πT/W1 - W₂.

Two parallel traveling plane waves have different angular frequencies w₁ and w2 and pressure amplitudes P₁ and P₂. (a) Show that the instantaneous energy density &; at a point in space varies between (P₁ + P₂)² / poc² and (P₁ – P₂)² / poc². (b) Show that the total energy density at the point averages to the sum of the individual energy densities of each wave alone. Hint: Let the averaging time be much greater than 2πT/W1 - W₂.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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and w2 and Two parallel traveling plane waves have different angular frequencies @1 pressure amplitudes P₁ and P₂. (a) Show that the instantaneous energy density %; at a point in space varies between (P₁ + P₂)² / poc² and (P₁ – P₂)² / poc². (b) Show that the total energy density & at the point averages to the sum of the individual energy densities of each wave alone. Hint: Let the averaging time be much greater than 2πT/|w1 - w₂|.
Transcribed Image Text:and w2 and Two parallel traveling plane waves have different angular frequencies @1 pressure amplitudes P₁ and P₂. (a) Show that the instantaneous energy density %; at a point in space varies between (P₁ + P₂)² / poc² and (P₁ – P₂)² / poc². (b) Show that the total energy density & at the point averages to the sum of the individual energy densities of each wave alone. Hint: Let the averaging time be much greater than 2πT/|w1 - w₂|.
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