Handbook for Sound Engineers

Acoustics for Auditoriums and Concert Halls 187

located in this indifferent acoustical boundary region, so
that the influence of this additional attenuation becomes
particularly relevant for the auditory impression.
According to Mommertz^45 this effect of additional
attenuation can be attributed to three causes:

1. The periodical structure of seat arrangement
   compels a guided wave propagation for low
   frequencies. In the frequency range between
   150 Hz and 250 Hz, this additional attenuation
   causes a frequency-selective level dip which is
   designated as seat dip effect. An example is given
   in Fig. 7-52 for a frequency of about 200 Hz.^45


2. The scattering of sound at the heads produces an
   additional attenuation especially in the frequency
   range between 1.5 kHz and 4 kHz, which is desig-
   nated as head dip effect, Fig. 7-52. The magnitude
   of the effect depends largely on the seat arrange-
   ment and the orientation of the head with regard to
   the sound source.


3. In combination with the incident direct sound, the
   scattering at the shoulders produces a very broad-
   band additional attenuation through interference. It
   is possible to define a simple correlation between
   the so-called elevation angle, Fig. 7-53, and the
   sound level reduction in the medium-frequency
   range at ear level of a sitting person.^45

(7-72)

where,

' L is in dB,

is in degrees, < 8°.

Fig. 7-54 shows a graphical representation of the
correlation resulting from Eq. 7-72. One sees that with a
plain arrangement of source and receiver the resulting
level reduction may be up to about 14 dB, whereas an

elevation angle of 7° suffices to cut the level reduction

to a negligible amount of less than 1 dB. The reflection

plane defined in Fig. 7-53 lies herewith hL=0.15m

(0.5 ft) below ear level, for example, at shoulder level of

a sitting person (approximately 1.05 m [3.5 ft] above

the upper edge of floor). According to Reference 45, the

additional attenuation depends herewith only on the

elevation angle, no matter if tier sloping is effected in

the audience area or in the performance area.

Fig. 7-55 shows the influence of the height of the

sound source above the ear level of a person sitting in a

row at a distance source-receiver of 15 m (50 ft), on the

frequency-dependent additional attenuation caused by a

grazing sound incidence over an audience.^45 The

receiver level is herewith 1.2 m (4 ft) above the upper

edge of the floor, the height of the source above the

floor is represented in this example as being 1.4 m and

2.0 m (4.6 ft and 6.6 ft). With a level difference of only

0.2 m (0.66 ft) between source and receiver, one can

clearly recognize the additional timbre change of the

direct sound component and of the initial reflections by

attenuation in the low- and medium-frequency ranges,

whereas with a level difference of 0.8 m (2.6 ft) the

sound level attenuations get reduced to below 3 dB.

Figure 7-52. Measured quantity spectrum of the transfer

function above a plain audience arrangement.^45

'L –= 20 log 0.2+0.1J

J J

100 1000 10,000

Frequency–Hz

10

0

10

20

30

40

Response–dB

Figure 7-53. Geometric data for determining the elevation

angle above a sound reflecting plane.

Figure 7-54. Sound pressure level reduction by sound

dispersion at shoulder level of sitting persons as a function

of the elevation angle.

hs = height of the sound source above the reflection plane

he = height of the receiver above the reflection plane

G = elevation angle

hs G

G

G

he

Elevation angle–degrees

Level reduction–dB

0 2 4 6 8

16

14

12

10

8

6

4

2

0