52. The nodes are located from vanishing of the spatial factor sin 5πx= 0 for which the solutions are 12350,,2,3,0,,,,555xxπ= π ππ¡=!"(a) The smallest value of xwhich corresponds to a node is x= 0. (b) The second smallest value of xwhich corresponds to a node is x= 0.20 m. (c) The third smallest value of xwhich corresponds to a node is x= 0.40 m. (d) Every point (except at a node) is in simple harmonic motion of frequency f= ω/2π= 40π/2π= 20 Hz. Therefore, the period of oscillation is T= 1/f= 0.050 s. (e) Comparing the given function with Eq. 16–58 through Eq. 16–60, we obtain 120.020sin(540 )and0.020sin(540 )yxtt=π−π+πfor the two traveling waves. Thus, we infer from these that the speed is v= /k= 40
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This note was uploaded on 04/16/2011 for the course PHYSICS 191262 taught by Professor Najafzadeh during the Spring '09 term at The Petroleum Institute.