and w2 and Two parallel traveling plane waves have different angular frequencies w₁ 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
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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5.8.1. Two parallel traveling plane waves have different angular frequencies w₁ and @2 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.
1
Transcribed Image Text:5.8.1. Two parallel traveling plane waves have different angular frequencies w₁ and @2 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. 1
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