Natural Science Forum / Physics / Acoustics / August 2005

    In oversimplified theory (e.g. Sabine absorption), the decay rate is
calculated using the average absorption in the room.

    In reality, the RT observed at any point in that room is the result of
the decay rate of the modes dominant in amplitude there. Note that
(except for very low frequencies) I said the plural, 'modes'.

    When there are multiple modes within the pass band, such as the 250 Hz
1/3 octave band, several room modes can occur within this pass band from
223 Hz to 281 Hz.

    At that moderately low frequency of 250 Hz, the wavelength is about
4.4' (1.3m). A changed position can see modes of different shapes and
damping. (A "mode shape" is just a map of the locations of the maximum
and minimum SPL for that specific mode.) It's the damping (AKA
'absorption') rate for each specific mode that determines the decay rate
(in dB/sec) of that specific mode.

    The damping, or decay rate, for each mode depends on the amount of
sound absorbing material located at the pressure maximums of the mode
shape. (Suspended volume absorbers also absorb at the sound velocity
maximums, found at and near sound pressure minimums.)
   
    The decay rate result found for this 250 Hz 1/3 octave band will be the
decay rate of the ensembled average energy of the group of modes
occurring in that 1/3 octave pass band. Movement from one location to
another will find a different amplitude distribution and accordingly a
different ensemble decay rate.

    Another interesting and often confounding result is that there are
often modes with fast decays (high absorption) and other modes in the
same pass band having a slow decay (low absorption), causing a
"two-slope" decay. The slow tail is always due to modes that experience
much less decay, such as a mode trapped between two parallel walls
having no absorption installed on them. Whether you select for
consideration the early (fast) decay or the later (slow) decay is a
matter of sound control strategy. Early decay is significant for noise
reduction measures. Late decay is of concern for speech intelligibility
where reverberating vowel sounds mask later sibilant sounds.

    In the 1950's, Fitzroy knew of the parsed x-, y-, z dimensionality, and
strove to compensate or represent it with his three- expression
refinement. His method more accurately estimates the decay rate to be
found in practical rooms having poor diffusion (most occupied rooms
these days). I have used this method consistently throughout the years
to control my architectural designs.

Back to the original question:
    Knowing that decay rates observed depend on modal structure in both the
frequency and spatial domains, one also expects a variation observed RT
for any band of frequencies when moving the microphone from one position
to another, and also when moving the source from one position to another.
    It is possible that when the measurement band is so narrow as to
encompass only one mode, that the variation with microphone position,
and the source position as well, will disappear.
    But one must be cautious of "degenerate modes" at moderate frequencies,
where two different modes can have identically the same frequency. Cubic
rooms are worst for this degeneracy. Rooms with two dimensions the same
are next worst, and rooms with three different dimensions have fewer
still such degenerate modes. It is also considered effective to have non
parallel walls so that modal definition becomes washed out or blurred.
    Thus, one can minimize the decay sensitivity to source positions by
constructing or selecting test rooms with non equal x, y, z dimensions
and non parallel walls.
    Common architecture (faced every day in consulting work) is less kind
in this regard.

        Angelo Campanella