University Physics with Modern Physics with Mastering Physics (11th Edition)

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15.70: a) The wave moving to the left is inverted and reflected; the reflection means that the wave moving to the left is the same function of , x - and the inversion means that the function is ). ( x f - - More rigorously, the wave moving to the left in Fig. (15.17) is obtained from the wave moving to the right by a rotation of ° 180 , so both the coordinates ) and ( x f have their signs changed. b). The wave that is the sum is ) ( ) ( x f x f - - (an inherently odd function), and for any . 0 ) 0 ( ) 0 ( , = - - f f f c) The wave is reflected but
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Unformatted text preview: not inverted (see the discussion in part (a) above), so the wave moving to the left in Fig. (15.18) is ). ( x f-+ d) dx x d x d x df dx x df dx x df dx x df x f x f dx d dx dy ) ( ) ( ) ( ) ( ) ( ) ( )) ( ) ( (---+ =-+ =-+ = . x x dx df dx df-=-= At = x , the terms are the same and the derivatives is zero. (See Exercise 20-2 for a situation where the derivative of f is not finite, so the string is not always horizontal at the boundary.)...
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