chapter 18 slides.pptx - Chapter 18 Superposition and...

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Chapter 18 Superposition and Standing Waves
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Learning Objectives Interference of waves Idea of superposition of waves Constructive and destructive interference Standing waves Periodic waves in between two boundaries Strings Air Electromagnetic waves Harmonics and modes Only certain allowed frequencies The idea of quantization Resonance Different types of air standing waves What kind of tube is it created in Beats
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Waves vs. Particles Waves are very different from particles. Particles have zero size. Waves have a characteristic size – their wavelength. Multiple particles must exist at different locations. Multiple waves can combine at one point in the same medium – they can be present at the same location. Introduction
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Quantization When waves are combined in systems with boundary conditions, only certain allowed frequencies can exist. We say the frequencies are quantized. Quantization is at the heart of quantum mechanics, studied later The analysis of waves under boundary conditions explains many quantum phenomena. Quantization can be used to understand the behavior of the wide array of musical instruments that are based on strings and air columns. Waves can also combine when they have different frequencies. Introduction
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Superposition Principle Waves can be combined in the same location in space. To analyze these wave combinations, use the superposition principle : If two or more traveling waves are moving through a medium, the resultant value of the wave function at any point is the algebraic sum of the values of the wave functions of the individual waves. Waves that obey the superposition principle are linear waves. For mechanical waves, linear waves have amplitudes much smaller than their wavelengths. Section 18.1
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Superposition and Interference Two traveling waves can pass through each other without being destroyed or altered. A consequence of the superposition principle. The combination of separate waves in the same region of space to produce a resultant wave is called interference. The term interference has a very specific usage in physics. It means waves pass through each other. Section 18.1
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Superposition Example Two pulses are traveling in opposite directions (a). The wave function of the pulse moving to the right is y 1 and for the one moving to the left is y 2. The pulses have the same speed but different shapes. The displacement of the elements is positive for both. When the waves start to overlap (b), the resultant wave function is y 1 + y 2. Section 18.1
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Superposition Example, cont When crest meets crest (c) the resultant wave has a larger amplitude than either of the original waves. The two pulses separate (d).
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