Handbook for Sound Engineers

128 Chapter 6

If we consider only the length of the room, we set q
and r to zero, their terms drop out, and we are left with

(6-2)

which looks familiar because it is the f 0 frequency of
Fig. 6-1. Thus, if we set p= 1 the equation gives us f 0.
When p=2 we get 2f 0 , with p=3, 3f 0 and so on. Eq.
6-1 covers the simple axial mode case, but it also
presents us with the opportunity of studying forms of
resonances other than the axial modes.
Eq. 6-1 is a 3D statement based on the orientation of
our room on the x, y, and z axes, as shown in Fig. 6-4.
The floor of the room is taken as the x plane, and the
height is along the z axis. To apply Eq. 6-5 in an orderly
fashion, it is necessary to adhere to standard termi-
nology. As stated, p, q, and r may take on values of zero
or any whole number. The values of p, q, and r in the
standard order are thus used to describe any mode.
Remember that:

• p is associated with length L.


• q is associated with width W.


• r is associated with height H.

We can describe the four modes of Fig. 6-1 as 1,0,0;

2,0,0; 3,0,0; and 4,0,0. Any mode can be described by

three digits. For example, 0,1,0 is the first-order width

mode, and 0,0,2 is the second-order vertical mode of the

room. Two zeros in a mode designation mean that it is

an axial mode. One zero means that the mode involves

two pairs of surfaces and is called a tangential mode. If

there are no zeros in the mode designation, all three

pairs of room surfaces are involved, and it is called an

oblique mode.

6.3 Modal Room Resonances

In order to better understand how to evaluate the distri-

bution of room modes, we calculate the modal frequen-

cies for three rooms. Let us first consider a room with

dimensions that are not recommended for a sound

room. Consider a room with the dimensions of 12 ft

long, 12 ft wide by 12 ft high (3.66 m × 3.66 m ×

3.66 m), a perfect cube. For the purposes of this exer-

cise, let us assume that all the reflecting surfaces are

solid and massive. Using Eq. 6-1 to calculate only the

Figure 6-2. Tangential room modes.

f c

2

---^1

L

---

©¹

§·

2

–=

c

2

---

1

L

©¹
=§·

1130

2 L

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

565

L

= --------- in feet

172

L

= --------- in meters

Figure 6-3. Oblique room modes.

Figure 6-4. The floor of the rectangular room under study is

taken to be in the xy plane and the height along the z axis.

Length (L)

Height

Width ( (H)

W)

x

y

z