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Sound System Design Reference Manual

Once the critical distance is known, the ratio of

direct to reverberant sound at any distance along thataxis can be calculated. For example, if the critical

distance for a talker is 4 meters, the ratio of direct toreverberant sound at that distance is unity. At a

distance of 8 meters from the talker, the direct soundfield will decrease by 6 dB by virtue of inverse squarelaw, whereas the reverberant field will be unchanged.

At twice critical distance, therefore, we know that theratio of direct to reverberant sound must be -6 dB. At

four times DC, the direct-to-reverberant ratio will

obviously be -12 dB.

Statistical Models vs. the Real World

We stated earlier that a confidence level of

about 10% allowed us to simplify our roomcalculations significantly. For the most part, this is

true; however, there are certain environments inwhich errors may be quite large if the statisticalmodel is used. These are typically rooms which are

acoustically dead and have low ceilings in relation totheir length and width. Hotel ballrooms and large

meeting rooms are examples of this. Even a largepop recording studio of more regular dimensions may

be dead enough so that the ensemble of reflectionsneeded to establish a diffuse reverberant field simplycannot exist. In general, if the average absorption

coefficient in a room is more than about 0.2, then adiffuse reverberant field will not exist. What is usually

observed in such rooms is data like that shown in

Figure 5-24.

Peutz (9) has developed an empirical equationwhich will enable a designer to estimate the

approximate slope of the attenuation curve beyondD

C in rooms with relatively low ceilings and low

reverberation times:

! 0.4 V

h T

 

60

" dB

In this equation, D  represents the additional fall-off in level in dB per doubling of distance beyond D

C.

V  is the volume in meters3, h  is the ceiling height in

meters, and T60

 is the reverberation time in seconds.In English units (V  in ft3 and h  in feet), the equation

is:

! 0.22 V

h T 

60

" dB

As an example, assume we have a roomwhose height is 3 meters and whose length and

width are 15 and 10 meters. Let us assume that thereverberation time is one second. Then:

! 0.4 450

3 1  = 2.8"

( )dB

Thus, beyond DC we would observe an additional

fall-off of level of about 3 dB per doubling of distance.

5-20

Figure 5-24. Attentuation with distance in a relatively dead room