Physical Modelling and Measurements of Plate Reverberation

In this article, the plate reverberation unit is studied. This effect unit has been intensively used in recording studios since the late 50's. From a mechanics point of view, this plate can be modeled by means of the Kirchhoff equations of motion of a thin linear plate. This basic model allows us to understand the common points and differences between the natural acoustic reverberation and the plate reverberation. Measurements on a EMT140 plate reverb are also presented and compared to the model predictions. The identification and modelling of the different damping mechanisms in the plate allows us to relate the reverberation time Tr to the plate physical parameters. In addition to the comprehension of the physics of the plate reverb, this work will be useful for physical modelling sound synthesis of this audio effect. INTRODUCTION Since the first days of broadcasting and recorded music, the artificial reverberation has been a very important tool for audio engineers. The use of close microphones to avoid noise suppresses the acoustics of the recording space. In 1926 RCA invented the reverberation chamber, the first tool to artificially replace the missing of reverberation energy. In the next 50 years, a lot of electromechanical devices were developed in order to create a reverberation effect in dry recordings [1]. One of the most acclaimed devices was the plate reverberation, in particular the EMT140 plate reverb. This unit is composed of a 2 m x 1 m size and 0.5 mm thickness flat rectangular steel plate. The plate is transversely punctually excited with an electric monophonic "dry" signal by means of an electro-dynamical actuator. The reverberated or "wet" stereophonic signal is read with two piezoelectric accelerometers that deliver an electric signal proportional to transverse punctual acceleration at two plate locations, the readout points. This unit has been extensively used by the music industry and it has become a classical effect very appreciated by audio engineers. Today, with the development of digital electronic reverberation units, using a plate reverberation in the studio has become difficult because of its fragility, bulky and expensive cost. The aim of this work is to understand the physics behind the plate reverberation in order to build a physical based sound synthesis algorithm. Physics-based sound synthesis allows very flexible means of control: the parameters which define the algorithm are directly related to the geometric and material properties of the real system. A PLATE MODEL The reverberation effect is produced by the plate undergoing small-amplitude vibrations. Because of the transverse excitation, the small thickness plate and the frequency range of use [20 Hz, 20 kHz], the behaviour of the plate vibrations can be modelled by the classical KirchhoffLove model for thin plate flexural vibrations [2]. For an isotropic material, the partial differential equation for the undamped plate is: