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# slides19all - kx sin ωt – p Beats – p Refection The...

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Previous lecture Wave Equation 2 D ∂x 2 1 v 2 2 D ∂t 2 =0 Traveling and standing waves Formulas: v = fλ, ω =2 πf, k =2 π/λ sin ³ ω ( t x/v ) ´ sin( ωt kx ) –p
Announcements 2 nd Hour Exam Tuesday Nov. 2 at 4:10 pm in Packard 101 Study Guide and Equation Sheet are on the web Practice Exam will be on the web by the end of the week –p

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Today Superposition Beat Frequency Refection o± waves Inter±erence –p
Mathematical Note If two waves are solutions to the wave equation, then so is their superposition (sum). We get a lot of mileage out of superposition. –p

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Superposition Any pulse can be written as a superposition of sines and cosines. –p
Trigonometry sin a +sin b = 2cos µ a b 2 sin µ a + b 2 sin a sin b = 2cos µ a + b 2 sin µ a b 2 –p

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Sum of traveling waves The sum of waves traveling to the left and right is a standing wave. sin( ωt + kx )+sin( ωt kx ) = 2 cos µ 2 kx 2 sin µ 2 ωt 2 = 2 cos

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Unformatted text preview: kx sin ωt – p. Beats – p. Refection The end oF the rope is ±xed. Wave is reflected with sign change. Imagine a wave with opposite sign coming from the other direction. – p. 1 Refection The end oF the rope is ±xed. Wave is reflected with sign change. Imagine a wave with opposite sign coming from the other direction. – p. 1 Refection The end oF the rope can move. Wave is reflected without change of sign Imagine a wave with same sign coming from the other direction. – p. 1 Refection The end oF the rope can move. Wave is reflected without change of sign Imagine a wave with same sign coming from the other direction. – p. 1 Interference – p. 1 Standing Wave BC • both ends fxed (violin string) • one end fxed, one open (organ pipe) – p. 1...
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slides19all - kx sin ωt – p Beats – p Refection The...

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