AP1200_Ch3_Waves-3Mechanisms-2007

AP1200_Ch3_Waves-3Mechanisms-2007 - 1 AP1200 3. Waves...

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Unformatted text preview: 1 AP1200 3. Waves Concepts AP1200 3. Waves Concepts 3.3 Wave mechanisms 3.3 Wave mechanisms Michel A. Van Hove Michel A. Van Hove WARNING: PRINTING THIS DOCUMENT WILL USE MUCH INK AND WILL NOT SHOW ANIMATIONS. 2 What is a wave? What is a wave? See also http://www.isvr.soton.ac.uk/SPCG/Tutorial/Tutorial/Tutorial_files/Web-basics-nature.htm, http://www.kettering.edu/~drussell/Demos/waves-intro/waves-intro.html A general definition : A wave is a collective motion of a medium around an equilibrium, often periodic, resulting from a disturbance, but self-sustained collective motion : many objects move together due to mutual interactions medium : the objects can form a solid, liquid, air, or be vacuum itself around an equilibrium : the objects try to return to their equilibrium positions (= rest positions) often periodic : many waves are repetitive (for some time) disturbance : an external source is needed to create a wave; it alone sets the frequency self-sustained : a wave can travel with no further input after the initial generation 6 3 How do waves work? Human waves How do waves work? Human waves wavelength space Medium: human chain without humans there is no human wave if one person is missing, the wave may stop Source: one person or group any person can be considered to be source (Huygens Principle) Mechanism: each person copies neighbors motion after a delay with humans this mechanism must be agreed beforehand Frequency: set by source if source changes its frequency, the wave also changes its frequency Note: same applies to dragon dance 9 4 source equilibrium Medium: string Source: shaking one end or point of string (in transverse direction) caution: no periodic shaking is used in piano, guitar, violin! there standing waves are excited with special frequencies using fixed ends Mechanism: each string element is pulled by its immediate neighbors wave shape is only maintained for small-amplitude waves damping possible amplification possible? Frequency: set by source How do waves work? Waves on a free string How do waves work? Waves on a free string 8 5 Waves on a free string: wave length and speed (1) Waves on a free string: wave length and speed (1) T T T- T + x y l A We can derive wave length and speed using , assuming a sine wave: To simplify the mathematics, we need to assume: the string is extremely thin (so it does not resist bending) the string does not stretch under tension (so it cannot change its length) the wave has a small amplitude A (so the string does not change its length when it deviates, each segments length l is unchanged when projected onto the x axis, and the restoring force F = T + + T- is parallel to the y axis) ma F = ( 29 t kx A y - = sin 6 6...
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AP1200_Ch3_Waves-3Mechanisms-2007 - 1 AP1200 3. Waves...

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