CHAPTER 17 INTERFERENCE OF WAVES AND THE CONSERVATION OF ENERGY In Section 17.2 we have seen how sound waves from two loudspeakers interfere with each other to produce a resultant sound wave that is the sum of the individual waves. The individual sound waves from the speakers carry energy as they move, and the resultant wave contains the same energy as the sum of the energies of the individual waves. This fact is consistent with the principle of conservation of energy, which we first encountered in Section 6.8. This principle states that energy can neither be created nor destroyed, but can only be converted from one form to another. One of the interesting consequences of interference is that the energy is redistributed, so there are places within a listening area where the sound is loud and other places where there is no sound at all. Interference, so to speak, “robs Peter to pay Paul,” but energy is always conserved in the process. Energy is also conserved when a standing wave is produced, either on a string or in a tube of air. The energy of the standing wave is the sum of the energies of the individual waves that comprise the standing wave. Once again, interference redistributes the energy of the individual waves to create locations of greatest energy (antinodes) and locations of no energy (nodes). The redistribution of energy also occurs when a wave is diffracted around an obstacle or the edges of an opening. As we have seen, diffraction is also an interference effect, one in which part of the energy of the wave is directed into regions that would not be accessible had interference not occurred. Interference and the redistribution of energy occurs for all types of waves, and we will see another example with light waves in Chapter 27. In all cases, the redistribution of energy that occurs is in accord with the principle of conservation of energy.
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