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Unformatted text preview: midterm 04 GADHIA, TEJAS Due: May 2 2007, 11:00 pm 1 Version number encoded for clicker entry: V1:1, V2:1, V3:4, V4:4, V5:5. Question 1 part 1 of 1 10 points A harmonic wave y = A sin[ k x t ] , where A = 1 meter, k has units of m 1 , has units of s 1 , and has units of radians, is plotted in the diagram below. +1 1 A (meters) x (meters) 10 20 30 At the time t = 0 Which wave function corresponds best to the diagram? 1. y = A sin bracketleftbiggparenleftbigg 2 3 m parenrightbigg x t parenleftbigg 2 3 parenrightbiggbracketrightbigg 2. y = A sin bracketleftbiggparenleftbigg 2 9 m parenrightbigg x t parenleftbigg 1 3 parenrightbiggbracketrightbigg 3. y = A sin bracketleftbiggparenleftbigg 2 3 m parenrightbigg x t parenleftbigg 5 3 parenrightbiggbracketrightbigg 4. y = A sin bracketleftbiggparenleftbigg 2 9 m parenrightbigg x t parenleftbigg 2 3 parenrightbiggbracketrightbigg 5. y = A sin bracketleftbiggparenleftbigg 2 3 m parenrightbigg x t parenleftbigg 1 3 parenrightbiggbracketrightbigg 6. y = A sin bracketleftbiggparenleftbigg 2 15 m parenrightbigg x t parenleftbigg 5 3 parenrightbiggbracketrightbigg 7. y = A sin bracketleftbiggparenleftbigg 2 9 m parenrightbigg x t parenleftbigg 4 3 parenrightbiggbracketrightbigg 8. y = A sin bracketleftbiggparenleftbigg 2 3 m parenrightbigg x t parenleftbigg 4 3 parenrightbiggbracketrightbigg 9. y = A sin bracketleftbiggparenleftbigg 2 9 m parenrightbigg x t parenleftbigg 5 3 parenrightbiggbracketrightbigg 10. y = A sin bracketleftbiggparenleftbigg 2 15 m parenrightbigg x t parenleftbigg 2 3 parenrightbiggbracketrightbigg correct Explanation: From the diagram of the wave function the wavelength = 15 m (6 horizontal scale di visions of 2 . 5 m each, see diagram below). Notice: Since one wavelength is 2 ra dians, each horizontal division is 2 6 = 3 radians. The given wave function (sine function with t = 0) y = A sin bracketleftbigg k x bracketrightbigg = A sin bracketleftbiggparenleftbigg 2 parenrightbigg x bracketrightbigg = A sin bracketleftbiggparenleftbigg 2 15 m parenrightbigg x bracketrightbigg (dark curve in diagram below) is shifted 2 divisions to the right (negative phase shift) of a nophaseshift sine function y = sin bracketleftbiggparenleftbigg 2 15 m parenrightbigg x bracketrightbigg (gray curve in diagram below), therefore = 2 3 = 2 3 radians . Checking the wave function y at x = 0, we have agreement with the diagram below y = sin parenleftbigg 2 3 parenrightbigg = . 866025 m ....
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 Spring '08
 Turner

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