Handbook for Sound Engineers

186 Chapter 7

The resonance frequency of a Helmholtz resonator is
generally calculated as

(7-70)

where,
c is the speed of sound in air, approximately 343 m/s
(1130 ft/s),
S is the cross-sectional area of the resonator in m^2 (ft^2 ),
V is the resonator volume in m^3 (ft^3 ),
l is the length of the resonator throat in m (ft),
2 ' l is the mouth correction.

In case of a square opening

,
where,
a is the edge length of the square opening.

For circular openings the resonance frequency fR in
Hz is calculated approximately from Eq. 7-70:

(7-71)

where,
R is the radius of the circular opening in m (ft),
V is the resonator volume in m^3 (ft^3 ),
l is the length of the resonator throat in m (ft).

7.3.4.4.4 Sound Absorption by the Audience

The efficiency of sound absorption by the audience
depends on many factors, for instance the occupation
density, the spacing of seats and rows, the clothing, the
type and property of the seats, the sloping of tiers and
the distribution of the persons in the room. In a diffuse
sound field the location of the sound source towards the
audience area is of minor importance in this regard. Fig.

7-50 shows a survey of the values of the equivalent

sound absorption area per person for a variety of occu-

pation densities and seating patterns in a diffuse sound

field. Since in many types of rooms the reverberation

time for medium and high frequencies is determined

almost exclusively by the sound absorption of the audi-

ence, one has to reckon with a rather high error rate, if

the range of dispersion of the factors influencing the

sound absorption capacity of the audience is to be taken

into account when determining the reverberation time,

Fig. 7-50. A still wider range of dispersion of the sound

absorption area occurs with the musicians and their

instruments, Fig. 7-51. The unilateral arrangement of

the listener or musician areas prevailing in most rooms

tends to disturb the diffusivity of the sound field heavily

so that the above-mentioned measured values may be

faulty, Figs. 7-50 and 7-51.

Especially with an almost plain arrangement of the

audience and performance areas there occurs for the

direct sound and the initial reflections a frequency-

dependent additional attenuation through the grazing

sound incidence on the audience area. This is intensified

by the fact that the sound receivers—i.e., the ears—are

Figure 7-49. General structure of a Helmholtz resonator.

s

V tt

l

t

I

fR

c

2 S

------ S

Vl + 2 'l

= -------------------------

2 'l|0.9a

fR

100*R

Vl +1.6R

|--------------------------------

* 30.5 for U.S. units

Figure 7-50. Equivalent sound absorption area in

m^2 /person of audience.

Figure 7-51. Equivalent sound absorption area in

m^2 /person of musicians.

2 persons/m1 person/m (^22) –wooden chairs, sitting–wooden chairs, sitting
0.2 persons/m0.2 persons/m^22 , sitting, standing
Frequency–Hz
100 1000 10K
1
0.8
0.6
0.4
0.2
Sound absorption area in m^0
2 /person
musicians with instruments:
1.1 mmusicians with instruments:^2 /person
2.3 m^2 /person
Frequency–Hz
100 1000 10K
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0
Sound absorption area in m
2 /musician