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In Reply to: RE: reflected waves posted by rick_m on June 04, 2007 at 23:28:29
I'll sit down later today and calculate this. For the moment, read this from the link in my previous post, which very emphatically states that sound waves reflected off of hard surfaces are polarity inverted:
http://www.physicsclassroom.com/Class/sound/u11l3c.html
These principles of free and fixed end reflection can be applied to sound waves. Though a sound wave does not consist of crests and troughs, they do consist of compressions and rarefactions. If a sound wave is traveling through a cylindrical tube, it will eventually come to the end of the tube. The end of the tube represents a boundary between the enclosed air in the tube and the expanse of air outside of the tube. Upon reaching the end of the tube, the sound wave will undergo partial reflection and partial transmission. That is, a portion of the energy carried by the sound wave will pass across the boundary and out of the tube (transmission) and a portion of the energy carried by the sound wave will reflect off the boundary, remain in the tube and travel in the opposite direction (reflection). If the end of the tube is "open" or uncovered such that the air at the end of the tube can freely vibrate when the sound wave reaches it, then the behavior at the boundary resembles free end reflection. There is no inversion of the disturbance when reflecting off the open end (uncovered end) of a cylindrical tube. That is, if a compression is incident towards an open-end, it will reflect and return as a compression. Similarly, if a rarefaction is incident towards an open end, it will reflect and return as a rarefaction. The opposite occurs if the end of the tube is "closed" or covered up. If the end of the tube is "closed" or covered, then the air at the end of the tube is fixed and cannot freely vibrate when the sound wave reaches it. In this case, the behavior at the boundary resembles fixed end reflection. There is inversion of the disturbance when reflecting off the closed end (covered end) of a cylindrical tube. That is, if a compression is incident towards an closed end, it will reflect and return as a rarefaction. Similarly, if a rarefaction is incident towards an closed end, it will reflect and return as a compression.
The behavior of sound waves at open ends and closed ends will become important Lesson 5 during the discussion of musical instruments. Many musical instruments operate as the result of sound waves traveling back and forth inside of "tubes" or air columns. These waves reflect at either a closed end or an open end of the air column; and the fact that inversion occurs at a closed end will have a huge impact on the numerical pattern of frequencies produced by such instruments.
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