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when two pebbles are thrown into a pond and hit the surface at different places, the Figure 18.1 is a pictorial representation of the superposition of two pulses. The wave function for the pulse moving to the right is y 1 , and the wave function for the pulse moving to the left is y 2 . The pulses have the same speed but different shapes, and the displacement of the elements of the medium is in the positive y direction for both 1 ! y 2 . When the crests of the pulses coincide (Fig. 18.1c), the resulting wave given by y 1 ! y 2 has a larger amplitude than that of the individual pulses. The two pulses finally separate and continue moving in their original The combination of separate waves in the same region of space to produce a resultant wave is called interference. For the two pulses shown in Figure 18.1, the displacement of the elements of the medium is in the positive y direction for both pulses, and the resultant constructive interference. Now consider two pulses traveling in opposite directions on a taut string where one pulse is inverted relative to the other, as illustrated in Figure 18.2. In this case, when 1 ! y 2 , but the values of the function y 2 are negative. Again, the two pulses pass through each other; however, be- cause the displacements caused by the two pulses are in opposite directions, we refer to destructive interference. SECTION 18.1 • Superposition and Interference 545 (c) (d) (b) (a) y 2 y 1 y 1 + y 2 y 1 + y 2 y 2 y 1 Active Figure 18.1 (a–d) Two pulses traveling on a stretched string in opposite direc- tions pass through each other. When the pulses overlap, as shown in (b) and (c), the net displacement of the string equals the sum of the displacements produced by each pulse. Because each pulse produces positive displacements of the string, we refer to their superposition as constructive interference. (e) Photograph of the superposition of two equal, symmetric pulses traveling in opposite directions on a stretched spring. Education Development Center , Newton, MA ▲ PITFALL PREVENTION 18.1 Do Waves Really Interfere? In popular usage, the term inter- Constructive interference Destructive interference (e) At the Active Figures link at http://www.pse6.com, you can choose the amplitude and orientation of each of the pulses and study the interference between them as they pass each other. |