# INTERFERENCE OF WAVES AND THE CONSERVATION OF ENERGY by gcw21244

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```									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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