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Please return your tests to me at the end of the peroid. I will return them Friday with a printout of all your scores and your current grade. Test scores – 110 possible Tomorrow finish the current lab series. Problems due Friday - Q1B.1 and Q1B.4

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Chapter Q1 Standing Waves

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Quantum Mechanics The laws of Newtonian mechanics do not hold for very small particles –Electrons, protons, neutrons, etc. Particles can act like waves, follow more than one path, pass through walls, and do other strange things. We begin by investigating waves in more detail.

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Types of waves A wave is a disturbance in a medium –Can be described by a function f(x,t) A tension wave can travel down a string A sound wave travels in a fluid –Both of these waves are described by a function such as: f x

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The superposition principle If two waves are traveling through a given medium, the function f(x,t) that describes the combined wave at any time t, is simply the algebraic sum of f 1 (x,t) and f 2 (x,t). –See figure Q1.3 –Note that the waves can pass through each other without changing either one.

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Reflection can occur at a node or an anti- node –In the case of a string carrying a wave, the fundimenal mode of vibration depends on whether or not the end of the string is fixed or free. Wave machine Figure Q1.5 –In the case of the resonance tube used in the speed of sound experiment The open end of the tube acts like the fixed end of a string –The pressure is fixed at atmospheric pressure. The bottom end of the tube acts like the free end of a string.

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Sinusoidal Waves Amplitude of the wave Wave number ω = angular frequency = 2πf f = frequency = number of waves per second λ = wavelength Wavelength = distance between wave crests. Period = T = 1/f = time between wave crests passing a given point. Phase velocity of a wave = v = λf = ω/k = λ/T = the velocity of the wave.

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Standing waves Waves traveling in the x direction Waves traveling in the –x direction node Anti-node

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Standing waves Case 1 – both ends fixed Case 2 – one end fixed, the other free n=1,2,3, … n=1,3,5, …

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Fourier Theorem Any wave shape can be made by adding a large (infinite) number of sinusoidal waves. –This is the FFT plot in the frequency experiment we did in lab.

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Resonance A system is sensitive to energy input at its normal modes of vibration. –To push a person on a swing, you get the best result when you push when they are at the top, starting down. –Six story buildings have a resonance with respect to earthquake waves

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Problems due Monday Q1B.1 and Q1B.4

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