P17_048 - 48. (a) The nodes are located from vanishing of...

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48. (a) The nodes are located from vanishing of the spatial factor sin 5 πx = 0 for which the solutions are 5 πx =0 ,π, 2 π, 3 π,. .. = x =0 , 1 5 , 2 5 , 3 5 ,... so that the values of x lying in the allowed range are x =0, x =0 . 20 m, and x =0 . 40 m. (b) Every point (except at a node) is in simple harmonic motion of frequency f = ω/ 2 π =40 π/ 2 π = 20 Hz. Therefore, the period of oscillation is T =1 /f =0 . 050 s. (c) Comparing the given function with Eq. 17-45 through Eq. 17-47, we obtain y 1 =0 . 020 sin(5 πx 40 πt )a n d y 2 =0 . 020 sin(5 πx +40 πt )
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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