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PHYS_2014_Lecture_26 - Lecture 26 Wave Motion 2 y x t = A...

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Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 26, Slide 1 ( ) ( ) , cos y x t A kx t ω = ± where k is the wave number 2 k π λ = ω is called the angular frequency 2 2 f T π ω π = = the ± sign designates whether the wave is moving to the left (+) or right (-) F v f T k λ ω λ μ = = = = Lecture 26: Wave Motion 2
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Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 26, Slide 2 Wave Interference Superposition of waves: The two waves are superposed on top of each other so that the net wave is the sum of the amplitudes of the two waves at each point along the string. Note: The two waves don’t interact with each other. 1. Waves approach each other. 2. Constructive Interference 3. Destructive Interference 4. Waves passed through each other.
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Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 26, Slide 3 Beats: Interference of Sound Waves Two waves having same amplitude, but slightly different frequency are traveling along the same string. Destructive Interference Constructive Interference
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Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 26, Slide 4 Wave Interference in 2 Dimensions Water waves from two sources in a ripple tank. Destructive Interference Constructive Interference
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Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 26, Slide 5 Wave Reflection Fixed End Loose End Force from wall: equal and opposite direction Force from rod: equal and opposite direction Destructive Interference Constructive Interference Pulse from wall is inverted Pulse from rod is same wall exerts force in both x and y rod exerts force only in x
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Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 26, Slide 6 Standing Waves ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 1 2 , cos , cos , cos cos cos cos 2sin sin 2 2 , 2 sin sin 2 2 , 2 sin sin , 2 sin sin y x t A kx t y x t A kx t y x t y y A kx t kx t kx t kx t kx t kx t y x t A y x t A kx t y x t A kx t ω ω ω ω α β α β α β ω ω ω ω ω ω = = − + = + = + + = − + + + = − = − = A continuous wave on a string is added to its reflection from a fixed end: trig. identity
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Fall 2010 Oklahoma State University PHYS2014: Benton Lecture 26, Slide 7 Standing Waves ( ) ( ) ( ) , 2 sin sin y x t A kx t ω = The term gives the amplitude of wave at a point x along the string.
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