ch16-p055 - 55. (a) The angular frequency is = 8.00/2 =...

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Nodes occur where cos( kx ) = 0 or kx = n π + π /2, where n is an integer (including zero). Since k = 1.0 π m –1 , this means () 1 2 (1.00 m) xn =+ . Thus, the smallest value of x which corresponds to a node is x = 0.500 m ( n =0). (e) The second smallest value of x which corresponds to a node is x = 1.50 m ( n =1). (f) The third smallest value of x which corresponds to a node is x = 2.50 m ( n =2). (g) The displacement is a maximum where cos( kx ) = ± 1. This means kx = n π , where n is an integer. Thus, x = n (1.00 m). The smallest value of x which corresponds to an anti- node (maximum) is x = 0 ( n =0). (h) The second smallest value of x which corresponds to an anti-node (maximum) is 1.00 m x = ( n =1). (i) The third smallest value of x which corresponds to an anti-node (maximum) is 2.00 m x = ( n =2). 55. (a) The angular frequency is ω = 8.00 π /2 = 4.00 π rad/s, so the frequency is
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