High Harmonic Content Research Articles

A proposed harmonic generator based on cyclotron waves

A cyclotron wave on a rectilinear filamentary beam can interact with a TE circuit mode of cylindrical symmetry propagating in synchronism with the beam. The interaction results in a periodic variation of the cyclotron transit angle of the electrons, causing a type of circumferential bunching which gives rise to high harmonic content. Provided the RF-field is adjusted to maximize a certain harmonic, its output power increases approximately as the square root of the harmonic number. The bunching is simply a redistribution of the relative positions of the various electrons constituting the original beam, and requires no supply of energy. All power delivered by the generator is therefore dissipated in the RF structure itself. The interaction mechanism is analyzed in detail, using two different approaches leading to the same final results. One is based on a wave description, the other considers the motion of the individual electrons. Possible applications for harmonic generation of high frequencies are discussed.

Transients in Pipe Organ Tones

A critical study of pipe organ sounds has been initiated by by recording transient and steady state waveforms and harmonic analyses of tones photographically from oscilloscope traces, with some magnetic tape recordings. Microphones are located from 34 to 112 in. from the mouth or open end of the pipe. Observations show that reed pipes usually reach maximum output in a fewer number of cycles than flue pipes, the number increasing with frequency at a rate less than proportional to frequency. Wave shape is roughly constant with time in reed pipes and in flue pipes with low harmonic content. Tones with higher harmonic content are usually initiated by an inexact harmonic, which grows and then often reduces in amplitude as the fundamental grows. In diapasons (open) this is second harmonic; in the Nason Flute (stopped) it is third. Third harmonic rise and early decay produces a “chiff” sound, less obvious with second harmonic. Reed pipe sounds approach impulse excitation of bandpass filters, with or without pronounced peaks. Flue pipes have peaked formants with regenerative excitation less rich in harmonics. The research objective must determine what is important in waveform as well as harmonic content, resulting in a better understanding of how we hear.