Building Acoustics

346 Building acoustics

The flanking sound reduction index Rf, involving the flanking element of area Si in the
sending (source) room and the corresponding one in the receiver room of surface area Sj,
we shall define as

(^) ()f S

1

ij ij 10 lg 10 lg 10 lg i.

ij ij j j

WI

RR

τ WI

⎛⎞ ⎛ ⎞ ⎛ ⎞⋅

==⋅ =⋅ =⋅⎜⎟ ⎜ ⎟ ⎜ ⎟

⎜⎟ ⎜ ⎟ ⎜ ⎟⋅

⎝⎠ ⎝ ⎠ ⎝ ⎠

SS

S

(9.24)

The quantity WS is the sound power incident on the partition, and Wij is the radiated
power from element j in the receiving room caused by vibration transmission from the
element i in the sending room. The sound intensity Ii is the intensity at the walls, assumed
to be the same at all surfaces in the sending room. The intensity Ij, however, is the one
radiated from the element j.

Ri Rj

Dij (Kij)

Rd

Ss

Wij

Ws

Si Sj

Figure 9.17 Sound transmission between two rooms, direct and flanking transmission paths.

Another choice, may be a more natural one, could be to use the actual area Si in the
definition given by Equation (9.24) in place of the area SS of the partition. The advantage
of using the latter, as pointed out in section 9.2.3, is that having a common reference area
for all transmission paths one may directly sum up the accompanying transmission
factors. The sound powers WS and Wij may as before be expressed as

2 2

S R

SS

00 00

and ,

44

ij

ij

p p

WS W

ρρcc

=⋅ = ⋅

 

AR (9.25)

where the sound pressure in the receiving room, having the total absorbing area AR, is
caused by flanking transmission only. The brackets indicate, as usual, a space averaging.
Inserting into Equation (9.24), we get

(^) SR() S
R
ij ij 10 lg.

S

RL L

A

=− +⋅ (9.26)