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**Unformatted text preview: **15.79: a) uk b) y t K x 2 (1 2) mvy m 1 2 y . t 2 A sin(kx t) and so uk 1 2 2 2 A sin (kx t). 2 c) The piece has width x and height x y , and so the length of the piece is x y x x 2 12 ( x) 2 x1 y x y x 2 2 12 x1 1 2 , where the relation given in the hint has been used. d) e) up y x F x1 1 2 ( y )2 x x x 1 F 2 y . x 2 kAsin(kx t), and so 1 2 2 2 Fk A sin (kx t) 2 2 v 2 2 F , shows that for a up and f) comparison with the result of part (c)with k 2 sinusoidal wave u k (f). uvp . g) In this graph, uk and up coincide, as shown in part At y 0, the string is stretched the most, and is moving the fastest, so u k and u p are maximized. At the extremes of y, the string is unstretched and is not moving, so u k and u p are both at their minimum of zero. h) uk up Fk 2 A2cos2 (t kx) Fk( v) A2 cos2 (t kx) P . v The energy density travels with the wave, and the rate at which the energy is transported is the product of the density per unit length and the speed. ...

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