Handbook for Sound Engineers

152 Chapter 7

most have a value of BR|0.9–1.0.

7.2.2 Energy Criteria

According to the laws of system theory, a room can be
acoustically regarded as a linear transmission system
that can be fully described through its impulse response
h(t) in the time domain. If the unit impulse G(t) is used
as an input signal, the impulse response is linked with
the transmission function in the frequency domain
through the Fourier transform

(7-13)

where,

As regards the measuring technique, the room to be
examined is excited with a very short impulse (delta
unit impulse) and the impulse response h(t) is deter-
mined at defined locations in the room, Fig. 7-7.

Here, the impulse response contains the same infor-
mation as a quasi-statically measured transmission
frequency response.
Generally, the time responses of the following
sound-field-proportionate factors (so-called reflecto-
grams) are derived from measured or calculated room
impulse responses h(t)

Sound pressure: (7-14)

Sound energy density: (7-15)

Ear-inertia weighted sound intensity:

(7-16)

where,
is 35 ms.

Sound energy: (7-17)

Basic reflectogram figures are graphically shown in

Fig. 7-8.

In order to simplify the mathematical and

measuring-technical correlations, a sound-energy-

proportional factor is defined as sound energy compo-

nent Ef. Being a proportionality factor of the sound

energy, this factor shows the dimension of an acoustical

impedance and is calculated from the sound pressure

response p(t).

(7-18)

where,

t' is in ms.

For determining a sound-volume-equivalent energy

component, t' has to be set to equal. In practical

rooms of medium size, t'|800 ms is sufficient.

For measuring of all speech-relevant room-acous-

tical criteria, an acoustic source with the

frequency-dependent directivity pattern of a human

Figure 7-7. Basic solution of signal theory for identification
of an unknown room.

G Z =Fht^`

ht =F1–^`G Z

1

2 S

------ G Z^ jZtdZ.

• f

+f

= ³

Impulse response

Dirac impulse

Black box (audience hall)

pt |ht

wt |h^2 t

JW 0 h^2 tc

Tc–t

©¹ ̈ ̧------------W 0

§·dtc

0

W

|³

W 0

Figure 7-8. Behavior of sound field quantity versus time

(reflectograms) for sound pressure p(t), sound energy

density w(t), ear-inertia weighted sound intensity

and sound energy Wt’(t).

Wt h^2 tcdtc

0

W

|³

JW 0 t

Sound energy component Et' p^2 t td

0

tc

=³

f