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Lesson_5.5_Printable

Lesson_5.5_Printable - Interference of Sound Waves Two...

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Interference of Sound Waves 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 . 1

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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. Waves meeting out of phase produce no sound The animation shows two sound waves interfering constructively in order to produce very large oscillations in pressure at a variety of anti-nodal locations . 2
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The illustration on the right shows two speakers in a room producing sounds of the same frequency and wavelengths. If you walk from A to B across the room, at some points the A B sound waves from s 1 and s 2 reach you in phase, so you hear a loud sound. Along the red lines, the compression of the wave from s 1 falls on the compression of the wave from s 2 , producing constructive interference. Along the green lines, the compression of the wave from s 1 falls on the rarefaction of the wave from s 2 , producing destructive interference. 4
The two waves are in phase (in step) and they interfere constructively producing loud sound. 5

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The two waves are completely out of phase (out of step) and they interfere destructively producing no sound. 6
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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? A B C path difference = BC - AC 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 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. 8
If the difference between the paths 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. For any integer n, the condition for two waves to meet in phase is that: A B C path difference = BC - AC Their path difference = n λ for constructive interference . Destructive interference happens when the path difference is an odd multiple of half of a wavelength. For destructive interference: The path differen (2 ce ) = 1 2 n λ + A path difference of λ is equivalent to phase difference of 2 π 9

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If there are 6 whole waves in the distance AC and 6.5 waves in the distance BC, when the wave from A starts a new waves at C, the wave from B has already set the particle at C in vibration half way through.
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