e represented by Eql 2. (II) Suppose two linear waves of equal amplitude and frequency have a phase difference o as they travel in the same medium. They can be represented by D = A sin(kx – wt) %3D D = A sin(kx – wt + ). bns 1oisllineo %3D sin 01 + sin 02 = (a) Use the trigonometric identity 2 sin (0, + 02) cos (0, – 02) to show that the resultant wave is given by %3D CoS (24 o sin kx- 2) D = (2A cos wt + %3D (b) What is the amplitude of this resultant wave? Is the wave purely sinusoidal, or not? (c) Show that constructive interfer- ence occurs if = 0, 2, 4T, and so on, and destructive interference occurs if o = T, 3T, 5T, etc. (d) Describe the resultant wave, by equation and in words, if o = T/2. %3D %3D

e represented by Eql 2. (II) Suppose two linear waves of equal amplitude and frequency have a phase difference o as they travel in the same medium. They can be represented by D = A sin(kx – wt) %3D D = A sin(kx – wt + ). bns 1oisllineo %3D sin 01 + sin 02 = (a) Use the trigonometric identity 2 sin (0, + 02) cos (0, – 02) to show that the resultant wave is given by %3D CoS (24 o sin kx- 2) D = (2A cos wt + %3D (b) What is the amplitude of this resultant wave? Is the wave purely sinusoidal, or not? (c) Show that constructive interfer- ence occurs if = 0, 2, 4T, and so on, and destructive interference occurs if o = T, 3T, 5T, etc. (d) Describe the resultant wave, by equation and in words, if o = T/2. %3D %3D

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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For testing purposes, a musical instrument manufacturing company creates a device so that when you blow into one end with your instrument, sound comes out the other end in opposite directions. A sound technician uses a whistle and generates sound waves with a frequency of 200 Hz. The waves travel in opposite directions in a sound studio, are reflected by end walls, and return. The studio is 50.0 m long and the whistle is located 14.0 m from one end. What is the phase difference (in degrees) between the reflected waves when they meet at the source of the sound? The speed of sound in air is 343 m/s.
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