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Unformatted text preview: 1 Lesson 5.5 Interference of sound waves. Lesson Objectives: At the end of this lesson students will be able to (i) interpret the concept of interference of harmonic sound waves and use it to explain phenomena such as beats and resonance. (ii) Use the concept of interference of sound waves to solve problems. Two sound waves advancing in the same medium will generate two separate displacements on the same set of particles. If the two waves are in phase, these displacements add up producing a larger displacement. Since the loudness of a sound is proportional to the square of the amplitude, this will give rise to a louder sound. If the two displacements are out of phase, the displacements they produce on the particles of the medium will cancel each other and the resultant wave will have no amplitude and hence no sound will be heard. Two waves meet in phase producing loud sound Fig. 1 Waves meeting out of phase produce no sound Fig. 2 You saw in lesson 1.4 that two waves differing in phase δ can be written as: s 1 = s o sin(kx – ϖ t) s 2 = s o sin(kx – ϖ t + δ ) 2 When these two waves meet at a point, the resultant wave is: ) 2 sin( 2 cos 2 2 1 δ ϖ δ + = + t kx s s s The resultant amplitude of the two waves is: 2 cos 2 s δ 1. Phase difference and path difference. If one wave starts from point A and another wave of the same frequency and wavelength starts from point B, how do we know if they are in phase or out of phase when they meet at point C? Remember that when a wave propagates in a medium, particles of the medium in intervals of one wavelength are in the same phase of vibration. If there are 50 whole waves A B C path difference = BC  AC Fig. 3 in the distance AC and 44 whole waves in the distance BC, then at C, the wave from A and the wave from B will be starting a new wavelength and so they will be in phase at C. In other words, if the difference between the path taken by the two waves to reach C (called the path difference) differs by an integer multiple of the wavelength, the waves will meet in phase. Therefore, the condition for two waves to meet in phase is that Their path difference = n λ for constructive interference . Where n is an integer. On the other hand, if there are 4 waves in the distance from A to C and 35.5 waves in the distance from B to C, when the wave from A starts a new 3 waves at C, the wave from B has already set the particle at C in vibration half way through. Therefore, the displacement on this particle due to wave from A will be opposite to that due to wave from B. Therefore, they cancel each other and there will be no wave at C. Thus destructive interference happens when the path difference is an odd multiple of half of a wavelength....
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This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.
 Fall '10
 George
 Physics

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