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Physics Lecture 10 - 3 Resonant mode(normal mode most...

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Lecture 10: The Physics of Music ---- Index of refraction: n = c/(speed of light in medium) Snell's Law (picture shown is light to different medium θ1 n1 n1sin(θ1) = n2sin(θ2) n2 θ2 Standing wave: λ(f) = velocity ---- I. Snell's Laws + Total internal reflection 1. n1sin(θ1) = n2sin(θ2) 1. if going from large to small index of refraction --> it is possible to have no refraction 2. Total Internal Reflection 1. the basic principle behind fiber optics 2. only works for light going from a higher to a lower index of refraction 3. extensively used in the telecommunications and medical industries 3. Snell's law in TIR 1. θ2 – arcsin(n1/n2 sinθ1) 1. If the argument is greater than 1 then there is no θ2 2. critical angle: n1/n2 sin(θcritical) = 1 solve for θ II. Standing Waves 1. oscillates in place 2. nodes are where the wave barely moves; antinodes are where all of the oscillation is
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Unformatted text preview: 3. Resonant mode: (normal mode) most symmetrical standing wave modes 1. sinusoidal in nature 4. end conditions (bound conditions) 1. node-node 2. antinode-antinode 3. node-antinode 5. fraction * wavelength = Length 6. Approach 1. draw a sketch of the mode 2. determine the wavelength from the sketch 3. determine the f from λ(f) = v where v = v prop for a traveling wave in the same system 7. Multiple Waves 1. add the wavelengths if they come to the same point (y total = y1 + y2) 1. y1 = A1sin(kx – ωt) y2 = A2sin(kx – ωt + Δ) 2. destructive interference (Δ = π): waves are opposite wavelengths 3. constructive interference (Δ = 0): waves are exactly the same and doubles the wave III. Beats 1. f beat = abs(f1 - f2)...
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