336 Building acoustics
addition, one will always get high radiation at frequencies around the so-called ring
frequency fR, the frequency where the circumference of the duct is equal to the
longitudinal wavelength of the duct material. Hence, the ring frequency of a circular duct
of diameter D is given by
(^) R L.
c
f
πD
= (9.10)
As the material of the duct is steel, for which the longitudinal wave speed cL is
approximately 5100 m/s, the ring frequency fR will in this case be approximately equal to
4600 Hz. It should be noted than one may treat the duct walls as ordinary plane surfaces
when the frequency exceeds the ring frequency.
9.2.3 Sound transmission involving suspended ceilings
A phenomenon related to the transmission by way of duct systems is transmission by
way of suspended ceilings. In many cases, the partition between two rooms just extends
to the ceiling (see Figure 9.10). The plenum chamber above the ceiling will then be
suitable for installing building service equipment such as cables and duct systems.
However, without taking proper precautions, the solution may give unsatisfactory sound
insulation. Despite the fact that this is a common construction both in schools and office
buildings, design tools for predicting the sound insulation are not satisfactory.
RS
RP
LS LR
h
HS
RR
Figure 9.10 Sound transmission between rooms involving a suspended ceiling and a common plenum. The
ceiling may as indicated include an absorber.
Probably, the first attempt to give a quantitative description was presented by
Mariner (1959), applying diffuse field models both for the rooms and the plenum. In
view of the fact that such plenums may have a height in the range 30–100 cm, maybe
including an absorber, the diffuse field assumption is normally not valid. Several
attempts have been made, partly by proposing simple corrections to the model of
Mariner, partly by developing quite different analytical models. Mechel (1995) has
presented a comprehensive theory, which composes the sound field by a forced wave
solution and a modal expansion of the field in the plenum. This is analogous to the
treatment of the duct transmission problem by Cummings (2001) (see the preceding