Lec-20 - -1 v 2 ∂ 2 D ∂t 2 = 0 – p The Wave Equation...

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Announcements Physics 19 begins We start waves today – p.
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A Word about the Exam Number of Students Score mean 51 range 8 - 96 – p.
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A Word about the Exam Number of Students Score mean 51 range 8 - 96 A B C – p.
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Today Waves: mathematical form Types of waves Wave Equation Demonstrations – p.
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Definition A wave is a time dependent “disturbance.” What is the disturbance? Sound wave: a travelling density variation in air or a material Water wave: wave height – p.
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Types of Waves Transverse and Longitudinal – p.
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Apply F = ma to section of rope xx + dx T ( x + dx ) T ( x ) Displacement D rope section of mass µ dx T = Tension in rope µ = linear mass density – p.
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The Wave Equation 2 D ∂x 2
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Unformatted text preview: -1 v 2 ∂ 2 D ∂t 2 = 0 – p. The Wave Equation ∂ 2 D ∂x 2-1 v 2 ∂ 2 D ∂t 2 = 0 ( v = speed of wave) – p. The Wave Equation ∂ 2 D ∂x 2-1 v 2 ∂ 2 D ∂t 2 = 0 ( v = speed of wave) It’s easy to show that a travelling pulse whose shape is given by an arbitrary function f , D ( x, t ) = f ³ t-x v ´ , is a solution to the wave equation. Just evaluate ∂ 2 D ∂x 2 = µ-1 v ¶ 2 f ±± ³ t-x v ´ = 1 v 2 f ±± ³ t-x v ´ and ∂ 2 D ∂t 2 = f ±± ³ t-x v ´ . – p. 1 D ( x, t ) = D sin( kx-ωt + φ ) – p. 1 Standing Waves – p. 1...
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Lec-20 - -1 v 2 ∂ 2 D ∂t 2 = 0 – p The Wave Equation...

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