Beat phenomenon at the arrival of a guided mode in a semi-infinite acoustic duct

Philippe Gatignol , Michel Bruneau (1) , Patrick Lanceleur , Catherine Potel (2, 1)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans
2 FANO - Fédération Acoustique du Nord-Ouest

A guided mode, generated at an initial time in the terminal section of a semi-infinite acoustic duct, will undergo dispersion effects during its propagation. It is well known (see [L. Brillouin, Wave Propagation and Group Velocity, Academic Press, 1960]) that at an observation point in the duct, after the arrival of a small precursor that moves with the speed of sound, the main part of the signal does arrive with the group velocity relative to the leading frequency. The axial propagation of the mode is governed by a Klein-Gordon equation and the problem may be solved by a Laplace transform. A careful numerical evaluation of the inverse Laplace integral in the complex plane shows that the amplitude of the mode yields oscillations at the first stage of its arrival. A steepest descent evaluation of the Laplace integral (see [M. Roseau, Asymptotic Wave Theory, North-Holland, 1976]) allows to explain that phenomenon in terms of beats between the main wave and the modes with neighboring frequencies.

Mots clés: Guided mode; Dispersion; Transient; Laplace transform

Domaines: Acoustique [physics.class-ph]

Philippe Gatignol, Michel Bruneau, Patrick Lanceleur, Catherine Potel. Beat phenomenon at the arrival of a guided mode in a semi-infinite acoustic duct. Acoustics 2012, Apr 2012, Nantes, France. ⟨hal-00811024⟩