P17_072 - 72(a The wave number for each wave is k = 25.1/m...

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72. (a) The wave number for each wave is k =25 . 1 / m, which means λ =2 π/k = 250 mm. The angular frequency is ω = 440 / s; therefore, the period is T =2 π/ω =14 . 3 ms. We plot the superposition of the two waves y = y 1 + y 2 overthet imeinterva l0 t 15 ms. The Frst two graphs below show the oscillatory behavior at x = 0 (the graph on the left) and at x = λ/ 8 31 mm. The time unit is understood to be the millisecond and vertical axis ( y ) is in millimeters. –1 0 1 5 10 15 t –2 0 2 5 10 15 t The following three graphs show the oscillation at x = λ/ 4 63 mm (graph on the left), at x =3 λ/ 8 94 mm (middle graph), and at x = λ/ 2 125 mm. –4 –2 0 2 4 5 10 15 t –2 0 2 5 10 15 t –1 0 1 5 10 15 t (b) If we think of wave y 1 as being made of two smaller waves going in the same direction, a wave y 1 a of amplitude 1 . 50 mm (the same as y 2 )andawave y 1 b of amplitude 1 . 00 mm. It is made clear in § 17-11 that two equal-magnitude oppositely-moving waves form a standing wave pattern. Thus, waves y 1 a and y 2 form a standing wave, which leaves y 1 b as the remaining traveling wave. Since the argument of y 1
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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