# ch16-p052 - 52 The nodes are located from vanishing of the...

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52. The nodes are located from vanishing of the spatial factor sin 5 π x = 0 for which the solutions are 123 50 , , 2 , 3 , 0 , , , , 555 xx π= π ππ ¡ = !" (a) The smallest value of x which corresponds to a node is x = 0. (b) The second smallest value of x which corresponds to a node is x = 0.20 m. (c) The third smallest value of x which 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 /2 π = 40 π /2 π = 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 12 0.020sin(5 40 ) and 0.020sin(5 40 ) yx t t π + π for 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.

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