AP1200_Ch3_Waves-3Mechanisms-2008

AP1200_Ch3_Waves-3Mechanisms-2008 - 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 How do waves work? Human waves How do waves work? Human waves wavelength space Type: usually transverse (can be longitudinal?) 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 Energy: not propagated! this is special: most types of wave propagate energy Frequency: set by source if source changes its frequency, the wave also changes its frequency Note: same applies to dragon dance 9 3 source equilibrium Type: transverse 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 Energy: propagated 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 4 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 5 We apply to the short string segment l , with F = T + + T- We set for the string segment, with the mass per unit length Using and , we get (see lecture notes): the wave length , resulting from the given frequency the speed (velocity) , independent of frequency! Note that wave length and speed increase with a higher string tension T and decrease with a lower mass per unit length These results are only correct under the assumptions made before!...
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AP1200_Ch3_Waves-3Mechanisms-2008 - 1 AP1200 3. Waves...

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