Lecture_26_PPT

Lecture_26_PPT - Chapter 16 Wave Motion Wave Equations k= 2...

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Chapter 16 Wave Motion
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Wave Equations () 2 (,) s i n yxt A x v t π λ =− 2 k = v = λ / T s i n2 xt A T ⎛⎞ ⎜⎟ ⎝⎠ animation
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String Model
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String Model
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String Model
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String Model
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String Model z The string is under tension T z Consider one small string element of length x z The net force acting in the y direction is (tan tan ) y BA FT θ Σ≈ y
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String Model z tan θ B = y / x at B z tan A = y / x at A (tan tan ) y BA FT Σ≈ y z tan B - tan A = ( y / x ) B –( y / x ) A z Σ F = m a y = µ ∆ x d 2 y /d t 2 z xd 2 y / dt 2 = T [ ( y / x ) B y / x ) A ]
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String Model y z µ ∆ xd 2 y / dt 2 = T [ ( y / x ) B –( y / x ) A ] z ( µ /T ) d 2 y / dt 2 = [ ( y / x ) B y / x ) A ]/ x () ( ) 2 2 BA yx y Tt x µ ∂∂ −∂∂ = ∂∆ 22 yy T tx ∂∂ =
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Linear Wave Equation 22 y y T tx µ∂ = z The wave functions y ( x , t ) represent solutions of an equation called the linear wave equation z This equation gives a complete description of the wave motion
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Linear Wave Equation 22 yy T tx µ∂ = () 2 (,) s i n yxt A x v t π λ =− ( µ /T ) v 2 y ( x,t ) = y ( x,t ) v 2 = T / µ
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Speed of a Wave on a String z The speed of the wave depends on the physical
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Lecture_26_PPT - Chapter 16 Wave Motion Wave Equations k= 2...

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