exam_1a_09_sol

# exam_1a_09_sol - Phys. 2306 Exam 1 F09 Form A Solutions...

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Phys. 2306 Exam 1 F09 Form A Solutions Consider a horizontal ( x ) wire of uniform mass/length μ = 0 . 153 g/cm. The wire is attached to a wall at one end and driven up and down ( y ) at frequency f= 2 . 00 Hz by a person ap- plying tension T at the other end. Let y ( x,t ) be the wave displacement. 1)If 2 y ( x,t ) ∂x 2 / 2 y ( x,t ) ∂t 2 = 0 . 255 (s/m) 2 , what is the tension in the wire in N? a)1.53 b)0.775 c)0.360 d)0.600 e)none of these The wave equation is 2 y ( x,t ) ∂x 2 - 2 y ( x,t ) ∂t 2 /v 2 = 0, where the wave speed v = q T/μ . Thus μ/T = 0 . 255 (s/m) 2 or T= 0 . 153(10 - 3 / 10 - 2 ) / 0 . 255 = 0 . 0600 N, (e). 2)If 2 y ( x,t ) ∂x 2 = 1 . 43 m - 1 what is the acceleration of the string at y ( x,t ) in m/s 2 ? a)5.61 b)2.37 c)2.83 d)8.02 e)none of these a= 2 y ( x,t ) ∂t 2 = 2 y ( x,t ) ∂x 2 / [ 2 y ( x,t ) ∂x 2 / 2 y ( x,t ) ∂t 2 ] = 1 . 43 / 0 . 255 = 5 . 61 m/s 2 , (a). 3)If the wave is sinusoidal, what is 2 y ( x,t ) ∂t 2 /y ( x,t ) in s - 2 ? a)158. b)83.7 c) - 83.7 d) - 158. e)none of these Here y(x,t)= A cos(2 π ( x/λ ± ft )). So a/y(x,t)= - (2 πf ) 2 = - [(2)(3 . 1415)(2 . 00)] 2 = - 158 s - 2 , (d). 4)If the wave is sinusoidal, what is y(x,t) in cm? a)1.42 b)3.55 c) - 1.42 d) - 3.55 e)none of these y(x,t)=-a/(2 πf ) 2 = - 5 . 61 / 158 . = - 0 . 0355 m = - 3.55 cm, (d). 5)Instead of being horizontal, suppose the wire was hanging vertically from the ceiling and the person drove the wire back and forth in the horizontal direction with frequency f at the wire bottom while applying the tension. Let μLg/T = 2 . 00, where L is the wire length and g is the acceleration of gravity. The ratio R of the wavelength halfway up the wire to the wavelength at the bottom is, a) R < 1 b)1 < R < 1 . 5 c)1 . 5 < R < 2 d) R = 1 e)none of these The tension at the bottom is T, but halfway up the tension is T+ μ Lg/2 because the wire has weight. Since v=

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## This note was uploaded on 12/24/2011 for the course PHYS 2306 taught by Professor Ykim during the Fall '06 term at Virginia Tech.

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exam_1a_09_sol - Phys. 2306 Exam 1 F09 Form A Solutions...

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