Sound transmission in buildings. Flanking sound transmission - Building Acoustics - page 349

The reduction indexes calculated are defined by the ratio of the power in the
bending wave transmitted to the power of the incident wave. These reduction indexes
need not be identical to the velocity level difference as defined above. It should also be
noted that the calculations do not account for longitudinal or transversal waves being
generated at the intersection.

Two auxiliary quantities were introduced as follows:

mB k mB

22 B2 21

ψ = and χ = = ,

(9.35)

4

mB k mB

11 B1 1 2

which is the ratio of the impedances and the ratio of the wavenumbers of the actual
plates, respectively. In practice, we shall normally find that the plates in line have
identical material and thickness. With this assumption one may express the reduction
indexes using a single parameter, which is the ratio of these auxiliary quantities. We then
get

ψ
χ =

Bc
Bc

2B1
1B2

,

(9.36)

where c B is the phase speed. If the plates involved have identical material properties, we
will further find that this ratio is given by the thickness ratio of the plates:

5
2

⎛⎞ ψ

χ

⎛⎞ h

h

2
1

= ⎜⎟

⎝⎠

.

(9.37)

⎜ ⎝⎠

Same material

The reduction indexes R 12 and R 13 for a T-junction are then given by

⎡ ⎤

2 χψ

ψ

R =⋅ 20 lg + ,

⎢ ⎥ 12

2 χ

⎣ ⎦

(9.38)

2

⎡ ⎤

⎛⎞ ⎛⎞ ψ 1 ψ

R =⋅ 10 lg 2 ⎢ + 2 +⋅ ⎥ .

⎜⎟ ⎜⎟ 13

χ 2 χ

⎢ ⎝⎠ ⎝⎠ ⎥

⎣ ⎦

The corresponding expressions applied to an intersection involving four plates are

⎡ ⎤

χψ
ψχ

R =⋅ 20 lg + + 3dB,

⎢ ⎥ 12

⎣ ⎦

(9.39)

⎡ ⎤

⎛⎞ ψ

χ

R =⋅ 20 lg 1 + + 3dB.

⎢ ⎜ ⎝⎠ ⎥ 13

⎣ ⎦

The above equations are depicted in Figure 9.19 assuming that all plates have
identical material properties. If this is not the case one has to substitute the dimension
ratio h 2 / h 1 by the quantity (ψ/χ) 2/5 , the latter with (ψ/χ) expressed by Equation (9.36). As
pointed out above, these reduction indexes are defined by the bending wave power, i.e.