Building Acoustics

132 Building acoustics

analysis; e.g. in a sound power determination in a reverberation room. In other cases, we
shall set up a sound field in a room with a loudspeaker driven by a narrowband signal. In
the latter case, we may alternatively measure the impulse response (between the
loudspeaker source signal and the signal from the microphone) using MLS or another
deterministic signal. The latter procedure is certainly superior when the task is to
determine differences in the squared sound pressures, e.g. when determining the airborne
sound insulation between two rooms.
Regarding a spatial averaged value as a reasonably global one for the room
presupposes that the room dimensions are of the same order of magnitude. This means
that in those rooms where the dimensions are too different, a corridor, an open plan
office or school, a factory hall etc., one will never, using a single source, find areas
where the sound pressure level is constant (in the statistical sense of the word). We will
experience a systematic variation; the sound pressure level will decrease more or less
rapidly with the distance from the source depending on the room shape, the absorption
and the presence of scattering objects. We shall return to this subject in section 4.9.
In most measurements standards, the required end result is the mean sound pressure
level and quantities derived from it. The underlying quantity, however, is the mean
squared pressure. In principle, we may proceed in two ways: We may sample the sound
field in a number M of microphone positions, which we in fact assumed when deriving
the expressions above, thereby calculating the mean sound pressure using the formula

2

1

2

0

10 lg (dB),

M

i

i

p

p

L

Mp

=

⎡⎤

⎢⎥

=⋅⎢⎥

⎢⎥

⎢⎥

⎢⎥⎣⎦

∑

(4.60)

where pi^2 denotes the time averaged squared pressure in position i. Alternatively, we may
use a microphone moving along a certain path in the room, performing a continuous
averaging process in time and space. We will then write

path

2

path 0

2

0

1

()

10 lg (dB),

T

p

ptdt

T

L

p

⎡⎤

⎢⎥

⎢⎥

=⋅⎢⎥

⎢⎥

⎢⎥

⎢⎥⎣⎦

∫

(4.61)

where Tpath is the time used for the complete path.
How do we compare these two methods as to the measuring accuracy? If a given
length of the path could be attributed to a certain equivalent number Meq of discrete
positions we could apply the equations given in section 4.5.2.1 directly for the
calculation of the standard deviation according to Equation (4.57). The time averaging
term σt should not give any problem as the total measuring time is Tpath = Ti ⋅ M, but how
long should the path be to correspond to M positions spaced at a distance ensuring
uncorrelated sampling? This may be calculated for frequencies above the Schroeder
frequency fS and for a circular path, which is the most practical one, we approximately
(perhaps not particularly surprising) get