Handbook for Sound Engineers

Sound System Design 1247

Q compares the on-axis sound intensity of a single
loudspeaker to what that intensity would be if the loud-
speaker were omnidirectional. Note that sound intensity
is proportional to the sound pressure LP squared.
Because Q is only defined for a single loudspeaker, any
mention of the off-axis Q or the Q of a cluster is techni-
cally inaccurate. A value for off-axis Q is useful,
however, in calculating Alcons (articulation loss of
consonents) for a listener not directly on-axis of a loud-
speaker. A value for the Q of a cluster could be useful to
help determine Alcons for a listener seated on-axis of a
single horn in a multihorn system. Thus, the concept of
Q is often extended to include these and other ideas.
The off-axis Q of a horn, for example, can be deter-
mined from an examination of the on-axis DI and the
difference in sound pressure level on axis versus
off-axis at the angle of interest. Subtract this difference
from the on-axis DI and convert back to Q. For
example, for a 90° (horizontal) horn, at 45° off-axis
horizontally, the SPL is 6 dB from its on-axis value.
Thus, if the on-axis DI is 12, the off-axis DI will be 6.
In general, if DI is known

(34-10)

Thus, the off-axis Q in this example is approximately 2.
The concept of the Q of a cluster is more difficult. In
theory, it would be possible to calculate the Q of a

cluster for a listener seated at any point in the room by

comparing the direct LP at that position with the overall

acoustic power output of the entire cluster. In practice,

this is a complex calculation since it requires a detailed

knowledge of the efficiency of each loudspeaker and the

electrical input to each driver as well as the directional

characteristics and efficiency of each horn and any

alterations that may be made in the horn’s directional

characteristics by the baffling effects of the cluster. One

way to deal with these problems is discussed in Section

34.3.2.10.2, where the calculation of Dc modifiers is

discussed.

34.2.3.2.3 Room Constant

Room constant, R (or Sa), is a measure of the relative

liveness of a room (a live room has a well-developed,

very audible reverberant field). A low room constant, or

low Sa, means a very live room. A high R or Sa means a

dead room. The R or Sa value depends on the size of the

room, so a specific value of R or Sa is not enough to

judge the reverberation characteristics of a room. Math-

ematically, room constant may be calculated as

(34-11)

where,

S is the total surface area of the room,

is the average absorption constant.

One version of the equation for critical distance uses

the room constant in place of the Sa term. While room

constant was commonly used to specify a room in the

past (in the Dc equation), it has fallen into disuse and is

usually replaced in most equations by the Sa term.

34.2.3.2.4 Critical Distance (Dc )

Dc (critical distance) is the distance from a source at

which the direct sound is exactly the same Lp as the

reverberant field, Fig. 34-7. Critical distance is impor-

tant in a number of concepts including intelligibility.

A good estimate of the critical distance for a loud-

speaker in a given room can be made by playing a

pink-noise source through the loudspeaker and walking

away from it holding a sound level meter. At some

distance, the LP will cease to change. Now walk back

toward the source until the LP increases exactly 3 dB.

That distance will be the critical distance. (Since the

direct sound and reverberant sound are equal here, the

total is 3 dB above the reverberant sound alone.) Crit-

Figure 34-6. Directivity, angular coverage, directivity index

(DI) and directivity factor (Q). Courtesy JBL Professional.

A. Q = 1. B. Q = 2.

C. Q = 4. D. Q = 8.

SPL

SPL + 3 dB

SPL + 6 dB

SPL + 9 dB

Omnidirectional

radiator

Same acoustical

power

SPL

SPL +D 1

E. Effect of directional

source.

Q 10

DI

------ 10

=

R Sa

1 – a

------------=

a