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Unformatted text preview: Optics, Waves, and Particles Physics 214, HW #04 Spring 2008 Problem 1. a) The initial length of the segment is L o = ( x + x ) x = x The length after the ends are displaced is L = [( x + x ) + s ( x + x,t )] [ x + s ( x,t )] Therefore, the change in length L is L = L L o = s ( x + x,t ) s ( x,t ) b) F = AY L L o = AY s ( x + x,t ) s ( x,t ) x c) Recalling the definition of the derivative, taking the limit x gives F ( x,t ) = AY s ( x,t ) x d) Apply Newtons Second Law, where m = o A x summationdisplay F = F ( x,t ) + F ( x + x,t ) = AY parenleftbigg s ( x,t ) x + s ( x + x,t ) x parenrightbigg = o A x 2 s ( x cm ,t ) t 2 Dividing both sides by o A x gives, 2 s ( x cm ,t ) t 2 = Y o parenleftBig s ( x + x,t ) x s ( x,t ) x parenrightBig x Taking the limit x gives 2 s ( x,t ) t 2 = Y o 2 s ( x,t ) x 2 1 Therefore, the wave speed is Y / o radicalbig . Problem 2. a) Recall that f n = v n = nv 2 L = n f 1 for n = 1 , 2 , 3 , We can find v with the information given for the case n = 1 . We know the fundamental frequency is f 1 = 150 Hz and the fundamental wavelength is 1 = 2 L = 2 ( 25 in ) = 2( 0.635 m ) = 1.27 m. Therefore, v = f 1 1 = 150 ( 1.27 ) m / s = 190.5 m / s b) f 2 = 2 f 1 = 300 Hz f 3 = 3 f 1 = 450 Hz c) If we press firmly, the length is reduced to...
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 Spring '08
 THORNE
 Physics

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