Handbook for Sound Engineers

Small Room Acoustics 139

an elegant way to model the reflections in a room. The

reflection can be considered to come from an image of

the source on the opposite side of the reflecting surface

and equidistant from it. This is the simple case: one

source, one surface, and one image. If this reflecting

surface is now taken to be one wall of a room, the

picture is immediately complicated. The source now has

an image in each of five other surfaces, a total of six

images sending energy back to the receiver. Not only

that, images of the images exist and have their effect,

and so on. A physicist setting out to derive the mathe-

matical expression for sound intensity from the source

in the room at a given receiving point in the room must

consider the contributions from images, images of the

images, images of the images of the images, and so on.

This is known as the image model of determining the

path of reflections. The technique is fully described in

Chapter 9.

6.7.3 Comb Filters

When the direct sound and a reflection combine at some
observation point, a spectral perturbation often called a
comb filter is produced. The frequency of the first notch
and the spacing of the rest of the notches is base on the
delay between the two arrivals. The first notch F in
hertz is calculated by

(6-6)

where,
t is the delay in seconds.

Each successive notch will be at

Fig. 6-16 shows the response of a system with a
delay of 1.66 ms between the two signals. Reflections
can dramatically change the way program material
sounds depending on the time of arrival, the intensity,
and the angle of incidence relative to the listener. For a
more in-depth treatment of how comb filters are
created, the reader is referred to reference 16.
In 1971 M. Barron wrote a paper exploring the
effects of reflections on the perception of a sound.^17 He
was trying to quantify the effects of lateral reflections in
concert halls. Although his work was conducted in large
reverberant spaces, a number of small room designers
look to his work with great interest as he is considering
the first 100 ms of a sound field in a room. In small
rooms that is often all you will get. Fig. 6-17 is a

graphic summary of the effects of a single lateral reflec-

tion. It can be seen that the very early reflections, on the

order of 0 to 5 ms, can cause image shifts even when

very low in amplitude relative to the direct sound. This

can be important as one considers, for example, the

accepted practice of placing loudspeakers on the meter

bridge of a recording console.

Fig. 6-18A shows an ETC of a popular nearfield

loudspeaker placed on the meter bridge of a recording

console, measured at the mix position. The first spike is

of course the direct arrival of the signal from the loud-

speaker. The second spike is the reflection off of the

face of the console, approximately 1.2 ms later. Fig.

6-18B shows the resulting frequency response when

these two signals arrive at the microphone. Finally C is

the frequency response of three loudspeaker with the

reflection removed. This author finds it curious indeed

that this practice of placing a loudspeaker on the

console ostensibly to remove the effects of the room and

get a more accurate presentation actually results in seri-

ously coloring the response of the speaker, and will

F^1

2 t

---- -=

1

t

---

Figure 6-16. Response of a system with a delay of 1.66 ms

between the two sources.

Figure 6-17. Graphic summary of the effects of a single

lateral reflection.

Disturbance

Spatial impression

Tone coloration

Threshold

Image shift

0

–10

–20

(^) 0 20 40 60 80 100
Reflection level relative to direct sound—dBDelay—ms
Image shift
Curve of equal
spatial impression