Building Acoustics

Sound transmission in buildings. Flanking transmission. 347

To be able to represent the reduction index Rij by the properties of the flanking elements
we shall make use of the fact that the power Wij may be expressed by the radiation factor
of the pertinent element on the receiving side. We shall write

WcSuij=ρ 00 j ^2 j σj, (9.27)

which together with the second Equation (9.25) gives us

22 2

2 00

R

R

4

.

jj j

ij

cS u

p

A

ρ σ

=



 (9.28)

A corresponding equation may be found for the sending room, linking the sound pressure
level and the velocity ui of the flanking element there, by using the transmission factor τi
of the flanking element. Hence, we shall write

22

t^00 00 S

ii S

,

ii i i i

i

W cS u cS u

WW W

ρ σρ σ

τ == =



(9.29)

where Wt and Wi denote the transmitted and incident power on the flanking element,
respectively. In the last expression, we have made use of the fact the sound intensity
everywhere is the same at all surfaces in the sending room. Using the expression for WS
(see Equation (9.25)), we get

22 2

2 00

S

4

.

ii

i

cu

p

ρ σ

τ

=



 (9.30)

Equations (9.24), (9.25), (9.28) and (9.30) then give

2

2

S

j jj

ij i

i i

u S

u S

σ

ττ

σ

= ⋅⋅⋅





(9.31)

or

2

S

10 lg 2 10 lg 10 lg ,

i i

ij i

j jj

u S

RR

u S

σ

σ

=+⋅ +⋅ +⋅





(9.32)

where Ri is the sound reduction index of the flanking element (wall or floor) in the
sending room. Whereas Ri tells us how easily the flanking element in the sending room is
excited into vibrations, the second term gives us the velocity level difference of the
respective elements when element i in the sending room is excited. We shall denote this
term by the symbol Dv,ij.
Following the standard EN 12354–1, we may instead define the flanking sound
reduction index as a mean value from measurements in two directions exchanging the
sending and receiving rooms. We shall then write