Page 159 - The Master Handbook Of Acoustics

134 CHAPTER SEVEN

the amount of loss in S) is dissipated as heat in wall reflections and
other boundary losses, along with a small amount in the air itself. With
a constant input to S, the sound-pressure level builds up as in Fig. 7-2B
to a steady-state equilibrium, even as an automobile traveling steadily
at 50 miles per hour with the accelerator in a given position. Pushing
down on the accelerator pedal increases the energy to the engine, and
the automobile stabilizes at a new equilibrium point at which the many
frictional losses are just supplied. Increasing the input to the source S
means a new equilibrium of room-sound-pressure level as room losses
are just supplied.

Decay of Sound in a Room

After opening the switch feeding source S, the room is momentarily
still filled with sound, but stability is destroyed because the losses
are no longer supplied with energy from S. Rays of sound, however, are
caught in the act of darting about the room with their support cut off.
What is the fate of the ceiling reflected component R 1? As S is cut
off, R 1 is on its way to the ceiling. It loses energy at the celling bounce
and heads toward H. After passing H it hits the rear wall, then the
floor, the ceiling, the front wall, the floor again, and so on . . . losing
energy at each reflection and spreading out all the time. Soon it is so
weak it can be considered dead. The same thing happens to R 2, R 3, R 4,
and a multitude of others not shown. Figure 7-2C shows the exponen-
tial decrease of the first bounce components, which would also apply
to the wall reflections not shown and to the many multiple bounce
components. The sound in the room thus dies away, but it takes a
finite time to do so because of the speed of sound, losses at reflections,
the damping effect of the air, and divergence.

Idealized Growth and Decay of Sound

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 result
in smooth growth and decay of sound. In Fig. 7-3A, the idealized
forms of growth and decay of sound in a room are shown. Here the
sound pressure is on a linear scale and is plotted against time. Figure