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Waves

Waves. Coupled Harmonic Oscillator (spring contraption) Pendulum Waves (pendulum waves.mov) Slinky (pulse, sine) SHO->Wave Animation (SHO ) Wave spreadsheet Wave terminology Wave equation derivation Wave Animation 1 (Transverse/longitudinal)

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Waves

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  1. Waves • Coupled Harmonic Oscillator (spring contraption) • Pendulum Waves (pendulum waves.mov) • Slinky (pulse, sine) • SHO->Wave Animation (SHO) • Wave spreadsheet • Wave terminology • Wave equation derivation • Wave Animation 1 (Transverse/longitudinal) • Traveling vs. Standing (Wave superposition)

  2. Spring contraption • Last Updated 9/05 - University of Texas at Austin Physics Department

  3. Wave animations • Spring Contraption • Pendulum Waves • Slinky (pulse, sine) • Generation of Wave • (SHO->Wave Animation) • Wave terminology • Excel Spreadsheet Animation

  4. Generation of Wave • amplitude • wavelength • frequency • period • velocity • transverse vs. longitudinal (animation)

  5. Excel Spreadsheet Animation • Y = A sin (kx – ωt) to right • Y = A sin (kx + ωt) to left • Snapshot in time • Motion at fixed position • Excel spreadsheet • v = f λ

  6. Deriving Wave Equation I

  7. Deriving Wave Equation II

  8. Wave Equation Summary • Can derive equation from F=ma (and a little calculus!) • Waves of form y = A sin(kx – ωt) are solution • Speed is v = sqrt (FT/μ) μ = mass/length

  9. Wave Examples • Problem 36 • Problem 37 • Problem 38 • Problem 41 • Problem 42

  10. Power in Traveling Wave • Energy proportional to Amplitude • Energy harmonic oscillator ½ k A2 • Waves in 3 dimensions • Intensity = power/area • Intensity = power/4π r2 • I2/I1 = 4π r12 / 4π r22 • Example 11-13

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