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See the Wikipedia article on vibrating strings:

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

This is only a rough approximation to the power cord situation, however, as the power cord is not a string in tension, and the acoustic waves are axial and not transverse. The notion that the cord has a fundamental resonant frequency and supports harmonics of it, still applies. This notion also applies to the electrical waves present on the cord.

If the cords are not treated to damp the acoustic resonances, then cords of different lengths will present different harmonic series to the equipment. Some lengths may allow the equipment to perform better than other lengths if their harmonic series do not excite internal resonant frequencies within the equipment.



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