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Homework 1 solutions - Duke Physics

**Physics** 143 Fall Term 2007 Due: September 3 HOMEWORK 1 Problem 1: Introduce Yourself By next Monday, please send me an email (schol@phy.duke.edu) introducing yourself, indicating: • Your major or planned major (if you know it). • Your long term professional interests (if you know them). • What physics courses and math courses you’ve had previously, at **Duke** or elsewhere. • Anything else you would like me to know about you, e.g. how to pronounce your name correctly, activities you are involved in, etc. Problem 2: Wave Review a. A cord has two sections with linear densities of 0.10 kg/m and 0.20 kg/m. An incident wave, given by D = (0.050 m) sin(0.6x − 12.0t), where x is in meters and t is in seconds, travels along the lighter cord. What is the wavelength on the lighter section of the cord? What is the tension in the cord? What is the wavelength when the wave travels on the heavier section? A travelling wave has the form: DDsin kx ωt. Wavelength can be derived from the coefficient of x: k 0.6m λ 10.5m We know that v T µ T µ . . 0.10 40N Tension and Frequency of the wave don’t change in each section. T µ v µ µ λ λ µ µ Page | 1‐3 10.5m . 7.40m . b. Suppose two linear waves of equal amplitude and frequency have a phase difference as they travel in the same medium. They can be represented by D1 = DM sin(kx −ωt) and D2 = DM sin(kx −ωt + ). Calculate the resultant wave. (Hint: it will help to make use of trig identities.) Is the resultant wave purely sinusoidal, or not? Explain. At what values of is there constructive interference? At what values of is there destructive interference? Describe the resultant wave, by equation and in words, if = π/2. DD D Dsinkx ωt Dsin kx ωt Use Trig Identity: sinθ sinθ2sin cos We obtain DD D 2 D cos 2 D cos sin sin kx ωt We know 2 D cos is a constant amplitude and sin kx ωt represents a purely sinusoidal wave. For constructive interference, the amplitude is a maximum, so cos 1 Therefore, 0, 2π, 4π, …

- Page 2 and 3: For destructive interference, the a