Ch16LecturesThursday, April 16, 2009

12:22 PM

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The following animation illustrates the interference of two waves travelling in opposite directions to produce

http://physics.info/interference/

The following animation illustrates the interference of two wave pulses travelling in opposite directions:

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http://phet.colorado.edu/en/simulation/wave-interference

http://www.physicsclassroom.com/mmedia/waves/swf.cfm

two waves travelling in opposite directions to produce a standing wave:

The following pages illustrate reflection of a wave from a boundary and the creation of standing waves:

http://www.acs.psu.edu/drussell/Demos/reflect/reflect.html

http://www.animations.physics.unsw.edu.au/jw/waves_s

The following animation illustrates interference of waves travelling in two dimensions (such as waves on the surface of water):

http://physics.info/waves-standing/

The following animation contrasts travelling waves and standing waves:

http://serc.carleton.edu/NAGTWorkshops/deepearth/activities/40826.html

The following animation illustrates more complex examples of interference for transverse waves:

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uperposition_reflection.htm#reflections

http://www.animations.physics.unsw.edu.au/jw/waves_superposition_reflection.htm#superposition

The following page illustrates standing waves:

http://en.wikipedia.org/wiki/Standing_wave

http://www.youtube.com/watch?v=4BoeATJk7dg

Video clip of standing waves on a string (captions in French):

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Standing sound waves in tubes

The previous discussion was about standing waves on strings, which are relevant for musical instruments such as guitars or pianos. However, wind instruments make sounds via standing sound waves, and for them there are more possibilities. For simplicity, model a wind instrument (flute, trumpet, etc.) by a straight tube filled with air. The tube could be open at both ends (which approximates a flute), open at one end and closed at one end (which approximates a trumpet), or closed at both ends (no musical instrument is like this, but the textbook includes this case for completeness). The standing waves on such simple tubes can be modeled as follows, where the amplitude of the wave represents pressure:

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OMIT Sections 16.5 AND 16.7

Interference of Waves from Two Sources

The basic simplifying assumption in this section is that the two sources are in phase.

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interference at points along the same line as the line joining the sources

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interference at other points•

Interference at points along the same line as the line joining the sources is illustrated in the following two figures. Note that the resulting interference pattern depends on the distance between the two sources. (Also note that the two sources have the same amplitude and are in phase.)

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In two or three dimensions, the pattern is more complex, as shown by the following figures:

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(Remember, we make the usual simplifying assumptions that the sources are in phase and have the same frequency.)

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