A String in a Room: Mixed-Dimensional Transfer Function Models for Sound Synthesis

Maximilian Schäfer, Rudolf Rabenstein, Sebastian J Schlecht
March, 2020
Cite Code

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 the spatial extent. In this contribution, we propose a technique for physical modeling of distributed sources and their radiation into the environment. In particular, we consider the modeling of a guitar string oscillating in a two-dimensional room. The room and the string rely on well established physical descriptions that are modeled in terms of transfer functions. The connection of string and room is given by a connection matrix that 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.

Type
Conference paper
Publication
International Conference on Digital Audio Effects (DAFx 2020)

A String is not a Point Source

In this first animation, we present the spatio-temporal behavior of a string:

In the next step, this string is picked up 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 spatial extent of the string is represented directly:

Connection Matrix

Figure 1: State-space description of a 1D string in a 2D room. The connection matrix T describes the modal connection between the string modes and the room modes.

The following animation demonstrates the dependency of the connection matrix 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.

Activate

Infotrackswitch.js - open source multitrack audio player
https://github.com/audiolabs/trackswitch.js

  • Play
  • Stop
  • Repeat
  • --:--:--:--- / --:--:--:---

Sound example with various configuration.

  • Only String
    • Solo
  • Point in a Room
    • Solo
  • String in a Room
    • Solo

The following audio examples varies the position of the string in the room.

Activate

Infotrackswitch.js - open source multitrack audio player
https://github.com/audiolabs/trackswitch.js

  • Play
  • Stop
  • Repeat
  • --:--:--:--- / --:--:--:---

Sound example with string configuration.

  • Position 1
    • Solo
  • Position 2
    • Solo
  • Position 3
    • Solo
  • Position 4
    • Solo
  • Position 5
    • Solo
  • Position 6
    • Solo
  • Position 7
    • Solo
  • Position 8
    • Solo
  • Position 9
    • Solo
  • Position 10
    • Solo

The following audio examples varies the position of the receiver in the room.

Activate

Infotrackswitch.js - open source multitrack audio player
https://github.com/audiolabs/trackswitch.js

  • Play
  • Stop
  • Repeat
  • --:--:--:--- / --:--:--:---

Sound example with receiver configuration.

  • Position 11
    • Solo
  • Position 12
    • Solo
  • Position 13
    • Solo
  • Position 14
    • Solo
  • Position 15
    • Solo
  • Position 16
    • Solo
  • Position 17
    • Solo

Credits

Trackswitch.js was developed by Nils Werner, Stefan Balke, Fabian-Rober Stöter, Meinard Müller and Bernd Edler.