Solitons, pulse splitting, and AM-FM conversion in cylindrical ducts

For propagation above cutoff in an acoustic duct, the dispersion is positive and weakly nonlinear effects are of two kinds. When the wavelength decreases with amplitude, a localized envelope propagates without spreading or distortion and the resultant final state is a soliton. Sloshing modes in a cylindrical duct of finite eccentricity belong to this class. When the wavelength increases with amplitude, a localized envelope splits into two disturbances moving with two different velocities of propagation. As a consequence, if a signal is amplitude modulated at the source, spatial beating between the two disturbances will occur, and at periodic positions in space the signal will become frequency modulated. Axially symmetric cross modes in a cylindrical duct of circular cross section belong to this class. A quantitative analysis of the results of the theory is presented along with its experimental consequences. (C) 1996 Acoustical Society of America.