Page 206 - Master Handbook of Acoustics

Sound pressure at the listener grows as one reflected component after another adds to the direct
sound and previous components. The sound pressure at L does not instantly go to its final value
because sound travels by paths of varying length. Given the speed of sound, reflected components are
delayed by an amount proportional to the difference in distance between the reflected paths and the

direct path. The growth of sound in a room is thus relatively slow due to finite transit time, but in
practice, sound growth is so fast as to be perceived as being instantaneous by a listener. On the other
hand, in comparison, sound decay is very slow and is usually readily heard (as reverberation) by a
listener. Therefore, the characteristics of sound decay are more important in practical room
acoustical design.
The ultimate level of sound in the room is determined by the energy from the source S. The energy

it radiates is dissipated as heat in wall reflections and other boundary losses, along with a small loss
in the air itself. With a constant input to S, the sound-pressure level grows, as shown in Fig. 11-1B, to
a steady-state equilibrium. Increasing the input to the source S yields a new equilibrium of room-
sound-pressure level versus room losses.

Decay of Sound in a Room

After turning off source S, the room is momentarily still filled with sound, but stability is destroyed
because the losses are not balanced by energy from S. Support is cut off to the rays of sound moving
through the room. Sound energy in the room begins to decay.

What is the fate, for example, of the ceiling reflected component R (see Fig. 11-1)? As S is cut
1
off, R is on its way to the ceiling. It loses energy at the ceiling reflection and heads toward L. After
1
passing L it strikes the rear wall, then the floor, the ceiling, the front wall, the floor again, and so on,
losing energy at each reflection. Soon it is so weak that it can be considered dead. The same thing
happens to R , R , R , and a multitude of other sound rays not shown. Figure 11-1C shows the
2
3
4
exponential decrease of the first reflection components, which would also apply to the wall
reflections not shown and to the many multiple reflection components. The sound in the room thus
dies away because of losses at reflections, the damping effect of the air, and divergence. However, it
takes a finite time to do so because of the speed of sound and the path lengths dictated by the room’s
dimensions.

Idealized Growth and Decay of Sound

Purely from the view of geometrical (ray) acoustics, the decay of sound in a room, as well as its
growth, is a stepwise phenomenon. However, in the practical world, the great number of small steps
involved results in smooth growth and decay of sound. Idealized forms of growth and decay of sound
in a room are shown in Fig. 11-2A. Here the sound pressure is shown on a linear scale and is plotted

against time. Figure 11-2B shows the same growth and decay, except that sound-pressure level is
plotted in decibels, that is, on a logarithmic scale.