A String In A Room: Mixed-Dimensional Transfer Function Models For Sound Synthesis
Abstract
Physical accuracy of virtual acoustics receives increasing attention due to renewed interest in virtual and augmented reality applications. So far, the modeling of vibrating objects as point sources is a common simplification which neglects effects caused by their spatial extent. In this contribution, we propose a technique for the interconnection of a distributed source to a room model, based on a modal representation of source and room. In particular, we derive a connection matrix that describes the coupling between the modes of the source and the room modes in an analytical form. Therefore, we consider the example of a string that is oscillating in a room. Both, room and string rely on well established physical descriptions that are modeled in terms of transfer functions. The derived connection of string and room defines the coupling between the characteristic string and room modes. The proposed structure is analyzed by numerical evaluations and sound examples on the supplementary website.
A String is not a Point Source
In this first animation, we present the spatio-temporal behavior of a string. Obviously, each point of the string oscillates in a different way:
In the next step, we show how a point source model of a string would excite a room. To this end, the string is picked up only at a certain position (dashed line) and emitted into a room via an omnidirectional source:
Now, instead of the point source modeling, the string object can be placed directly in the room such that the full spatial extent of the string is represented:
Connection Matrix
Figure 1: State-space description of a 1D string in a 2D room. The connection matrix $\mathbf{T}$ describes the modal connection between the string modes and the room modes.
The following animation demonstrates the dependency of the connection matrix $\mathbf{T}$ on the spatial position of the string. The string position is rotated in each frame (while the absolute position in the room is similar to the animation above). The top right plot depicts the transfer function of the string (blue) and the resulting transfer function in the room at a pickup position (red):
Audio Examples
We present various sound examples of a string in a room. First, the basic sound examples for string only, point in a room and string in a room with the same configuration as in the animations above.
Sound example with various configuration.
The following audio examples varies the position of the string in the room.
Sound example with string configuration.
The following audio examples varies the position of the receiver in the room.
Sound example with receiver configuration.
Credits
Trackswitch.js was developed by Nils Werner, Stefan Balke, Fabian-Rober Stöter, Meinard Müller and Bernd Edler.