2010 PHYSICS 002C Lecture 07

# 2010 PHYSICS 002C Lecture 07 - PHYSICS 002C Lecture 06...

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PHYSICS 002C Lecture 06 April 09, 2010 Serway and Jewett Chapter 14.1-4 Interference Clicker Q1: The principle of superposition holds for a wave equation which is a) pliniar; b) finial; c) linear; d) similar e) linial. Clicker Q2: Interference occurs when two waves in a medium a) haplap; b) underlap; c) overlap; d) dewlap; e) lapstreak. Clicker Q3: A single frequency standing wave exhibits harmonic motion a) whenever it is a combination of two wavelengths; b) nowhere; c) everywhere except at the nodes; d) only at the antinodes; e) only at the nodes. One type of interference Chap 14.1 The Superposition Principle The sum of two solutions to a linear wave equation is also a solution. The definition of a linear operator b ( x , y ,…) that acts on a set of functions f ( x , y ,…), g ( x , y ,…), … is that b ( x , y ,…) [ af ( x , y ,…)+ bg ( x , y ,…)]= Searchlight beams passing through each other a b ( x , y ,…) f ( x , y ,…)+ b b ( x , y ,…) g ( x , y ,…) for all functions in the set and for all multipliers a , b , …. A linear wave equation is of the form b ( x , y ,…, t ) f ( x , y ,…, t )=0, so a sum of two solutions f ( x , y ,…)+ g ( x , y ,…) is also a solution. Examples : Electromagnetic waves (light, radio, x-rays) in vacuum. Two light beams scatter from each other (especially if their frequency is near m e c 2 / h = 1.23559 10 20 Hz). Superposition works if the amplitude is small even for a nonlinear wave equation. Gravity waves are inherently nonlinear because a gravitational field is a source for more gravitational field: field ( x , y , z , t )= g ( x , y , z , t ) 2 /8 c 2 . Light waves in optical fibers are nonlinear at high amplitudes.

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2010 PHYSICS 002C Lecture 07 - PHYSICS 002C Lecture 06...

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