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Continuous spectrum is result of vibrations with different frequency of electric charges (maybe free electrons) of the surface of materials which aren't in gas (or vaper) phase.
Are you sure this is the definition of continuous spectrum?I don't think so as I just read the chemistry text regarding this continuous spectrum.The continuous spectrum(lines) as stated there is that it consist of all the lines of all wavelength and frequency.eg.the sunlight.correct me if I was wrong.
It's right. all lines means all wavelengths these differences in wavelengths or frequencies are because of different frequencies of vibration of electric charges which produce an electric field and a magnetic field in the space perpendicular to each other as shown here: http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=35
It's all about classic point of view.
Generation of electromagnetic waves is also described in lecture #30 of 8.02 SC by Professor Walter Lewin.