Wave Propagation in a Dispersive and Emissive Medium

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Abstract
Recently a measurement of the velocity of longitudinal ultrasonic waves propagating through a phonon maser amplifier showed that the pulse traveled with the maximum or cutoff velocity at resonance. With an approximate dispersion rule for a homogeneously broadened spin-resonance transition, the propagation of the wave is analyzed using a method for the asymptotic expansion of Fourier-type integrals. This analysis, contrary to earlier studies, indicates that the pulse observed, or at least the leading edge of that pulse, was an amplified precursor (transient response). For a sinusoidal imput signal, the asymptotic wave form at a given position is given for all possible values of the time.