Handbook for Sound Engineers

Computer Aided Sound System Design 1355

mesh correspond with the upper frequency handled by

the FEM. The higher the frequency, the smaller the

dimensions and the longer the calculation time. As an

example, to build a mesh in a hall of 10,000 m^3 you

need a mesh resolution of about 280,000 subvolumes to

apply the FEM up to 500 Hz. Fig. 35-20 shows such a

mesh grid for a church model. For the BEM only the

surface must be meshed accordingly.

After the mesh is ready and that is a quite difficult job
in complex room structures,^26 we need to know the
impedance behavior of the single wall parts. This is
again quite complex because any stiffness or mass
values of the majority of the wall materials are not
known. So in a first approach the impedance of the wall
material can be derived from the known absorption coef-
ficient. Now by applying the well-known algorithm of
the FEM, the transfer function at selected receiver places
may be calculated. By means of a Fourier transformation
you obtain the impulse response in the time domain. By
means of this method, transfer functions at receiver
places may also be calculated, even if the receiver is
shadowed from the sending position and the direct sound
was only coming by diffraction to the receiver.
This method can be used very well in small rooms
below 300 Hz. A mesh of a control room of 135 m^3
consists only of around 1000 subvolumes, if frequencies
higher than 300 Hz are neglected. This way very fast
calculation results can be expected.

35.1.5 Receivers and Microphone Systems

35.1.5.1 Human Ears

The properties of the human ears are explained in a lot

of books about psychoacoustics, including Chapter 3 of

this handbook. In simulation programs the acoustic

properties of a room or the free-field environment are

determined by calculation of the so-called impulse

response. This response is calculated using ray-tracing

methods. For a single point in space, the so-called mon-

aural response is determined, and the result supplies not

only the level at the receiver place, but also the fre-

quency dependence, the angle of incidence for single

reflections, and the run-time delay in comparison to the

first incoming signal (direct sound). Using so-called

head-related transfer functions (HRTF) measured with

dummy heads, or using in-ear microphones, Fig. 35-

21,^27 the monaural impulse response may be converted

into a binaural one used for real-time convolution, see

Section 35.3.3.

35.1.5.2 Microphones

The use of microphones in sound reinforcement systems

requires observation of a number of conditions. To

avoid positive acoustic feedback, it is frequently neces-

sary to keep the microphone at closer distance to the

sound source so that often considerably more micro-

phones have to be used. Moreover the live conditions

demand very robust microphones.

To simulate the use of microphones, to precalculate

the acoustic feedback threshold or to simulate enhance-

ment systems based on electronic processing, an exact

knowledge of the properties of the microphone types and

their connection technique is needed.

Basic Parameters. The microphone data are laid down

in standards.^28 In this context we will consider only this

data that is important for computer modeling. For fur-

ther information especially, regarding the types of

microphones, please refer to Chapter 16.

The magnitude of the output voltage of a micro-

phone as a function of the incident sound pressure is

described by the microphone sensitivity

Figure 35-20. Meshed model in EASE 4.2.

Figure 35-21. HRTF balloon of the left ear of a dummy

head.