Handbook for Sound Engineers

Small Room Acoustics 127

6.1 Introduction

The acoustics of small rooms is dominated by modes,

shape, and reflection management. Acousticians who

build large rooms are frequently frustrated with small

room design because few of the intellectual tools of the

trade that work in large rooms can be applied to small

rooms. Getting small rooms to sound right involves art

and science. The science part is mostly straightforward.

The creative part is quite subjective and a great

sounding small room can be just as elusive as a great

sounding concert hall.

6.2 Room Modes

A room mode is a phenomenon that occurs whenever
sound travels between two reflecting surfaces where the
distance between the surfaces is such that the impinging
wave reflects back on itself creating a standing wave.
The distribution of modes determines the low frequency
performance of a small room. Consider a sound source
S emitting a sinusoidal signal between two isolated
reflecting surfaces as in Fig. 6-1. Starting at a very low
frequency, the frequency of the oscillator driving the
source is slowly increased. When a frequency of
f 0 = 1130/2L (in feet) is reached, a so-called
standing-wave condition is set up. Consider what is
happening at the boundary. Particle velocity must be
zero at the wall surface but wherever particle velocity is
zero, pressure is at maximum level. The wave is
reflected back out of polarity with itself, that is to say
that the reflection is delayed by ½ of the period. This
results in a cancellation that will occur exactly midpoint
between the reflecting surfaces. If the walls are not
perfect reflectors, losses at the walls will affect the
heights of the maxima and the depths of the minima. In
Fig. 6-1 reflected waves traveling to the left and
reflected waves traveling to the right interfere, construc-
tively in some places, destructively in others. This effect
can be readily verified with a sound level meter which
will show maximum sound pressures near the walls and
a distinct null midway between the walls.
As the frequency of the source is increased, the
initial standing-wave condition ceases, but at a
frequency of 2f 0 another standing wave appears with
two nulls and a pressure maximum midway between the
walls. Other standing waves can be set up by exciting
the space between the walls at whole number multiples
of f 0. These are called axial modes as they occur along
the axis of the two parallel walls.

The two walls of Fig. 6-1 can be considered the east
and west walls of a room. The effect of adding two

more pairs of parallel walls to enclose the room is that

of adding two more axial standing-wave systems, one

along the east-west axis and the other along the vertical

axis. In addition to the two axial systems that are set up,

there will be a standing wave associated with two times

the path length that involves all four surfaces. These

modes are called tangential modes, Fig. 6-2. Most

rooms will have six boundaries and there are modes that

involve all six surfaces as well, Fig. 6-3. These modes

are called oblique modes.

In 1896 Lord Rayleigh showed that the air enclosed

in a rectangular room has an infinite number of normal

or natural modes of vibration. The frequencies at which

these modes occur are given by the following equation:^1

(6-1)

where,

c is the speed of sound, 1130 ft/s (or 344 m/s),

L is the length of the room in feet (or meters),

W is the width of the room in feet (or meters),

H is the height of the room in feet (or meters),

p, q, and r are the integers 0, 1, 2, 3, 4, and so on.

Figure 6-1. The simplest form of room resonance can be

illustrated by two isolated, parallel, reflecting wall surfaces.

S

Reflecting

wall

Reflecting

wall

L–Ft

f 0 = 1130

2 L

= 565

L

Distance–ft

Distance–ft

Distance–ft

Distance–ft

f 4 =4f 0

f 3 =3f 0

f 2 = 2f 0

Soundpressure

Soundpressure

Soundpressure

Soundpressure

f

c

2

--- p

L

©¹§·---^

(^2) q
W
©¹§·---- -
(^2) r
H
©¹§·--- -
2
= ++