Building Acoustics

Sound transmission 261

2

00

n 2

00

4

10 lg.

caF

L

pA

⎧ ρ ⎫

=⋅⎨ ⎬

⎩⎭



(6.125)

For the sound reduction index we shall be looking for an expression for the
proportionality factor b, the relationship between the velocity of the floor and the driving
sound pressure. By definition, the sound reduction index is given by

2

i

2

ii 00

2222

t0 0 00

4

10 lg 10 lg 10 lg ,

4

p

S

Wpc

R

WcSu cu

ρ

ρ σρσ

=⋅ =⋅ =⋅







(6.126)

where the radiation factor is included in the transmitted power Wt. Setting this factor
equal to one, and furthermore, using Equation (6.120) we get

(^22)
00

1

10 lg.

4

R

ρcb

=⋅

⋅

(6.127)

Combining this expression with Equation (6.125) and using Equation (6.122), we obtain

22 22

n 222

00 000

10 lg 10 lg.

4

kF f F

LR

pA cpA

π

π

⎡ ⎤⎡⎤

+=⋅⎢ ⎥⎢⎥=⋅

⎣ ⎦⎣⎦



(6.128)

Inserting for the reference values together with the force from the tapping machine, the
latter given by Equation (6.71), we arrive at a very simple expression applying to
measurements in one-third-octave band

LRn+≈ ⋅ +30 lgf38 dB. (6.129)

It should be noted that we have applied the point-to-point relationship according to the
principle of reciprocity in a situation where both sound pressure and velocity are mean
values taken over a room and a surface, respectively.
As seen from the examples shown in Figure 6.33, which are results from laboratory
measurements, Equation (6.129) gives a very good prediction in the case of a massive
concrete floor with the top cover. However, the fit is not particularly good for the hollow
concrete floor, which may be caused by the non homogeneity of this type of floor. As
shown earlier in Figure 6.20, we found that the impact sound pressure level of this type
of floor exhibited quite another frequency characteristic than the homogeneous one.
We shall also call attention to two other conditions that must be fulfilled applying
Equation (6.129). First, the transmission must take place only through the floor, i.e. the
flanking transmission must be negligible. Second, we have assumed when deriving
Equation (6.129) from Equation (6.128) that the force from the tapping machine is not
reduced by any kind of elastic layer, a floating floor etc. Constructions intended for
reducing impact sound will be treated in Chapter 8; here we just wanted to illustrate the
effect of such measures.
In fact, we could have used expressions derived earlier to arrive at this relationship
between the sound reduction index and the impact sound level. If we sum the expressions