# Doppler effect of a planar vibrating piston: strong solution, series expansion and simulation

1 S3AM - Systèmes et Signaux Sonores : Audio/Acoustique, instruMents
STMS - Sciences et Technologies de la Musique et du Son
Abstract : This article addresses the Doppler effect of a planar vibrating piston in a duct, as a plane wave radiation approximation generated by a loudspeaker membrane. This physical model corresponds to a nonlinear problem, because the linear propagation is excited by a moving boundary condition at the piston face: this introduces a varying propagation time between the piston and a fixed receiver. The existence of a regular function that solves the problem (a so-called strong'' solution) is proven, under a well-posed condition that guarantees that no shock occurs. This function satisfies an implicit equation to be solved. An algorithm based on the perturbation method is proposed, from which an exact solution can be built using power series. The convergence of the power series is numerically checked on several examples. Simulations derived from a truncated power series provide sound examples with audible intermodulation and distortion effects for realistic loudspeaker excursion and speed ranges.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01550622
Contributor : Tristan Lebrun <>
Submitted on : Thursday, June 29, 2017 - 4:55:16 PM
Last modification on : Thursday, March 21, 2019 - 1:21:04 PM

### Identifiers

• HAL Id : hal-01550622, version 1

### Citation

Tristan Lebrun, Thomas Hélie. Doppler effect of a planar vibrating piston: strong solution, series expansion and simulation. Conference on Digital Audio Effects, Sep 2017, Edimbourg, United Kingdom. ⟨hal-01550622⟩

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