L-ACOUSTICS V-DOSC Manual Version 4
6/29/2005
Page 142 of 158
APPENDIX 1:
WHY DO SEPARATED SOUND SOURCES INTERFERE?
When two sources are physically separated, the different arrival times of the wavefronts
radiated by the individual sources cause frequency- and position-dependent constructive and
destructive interference.
Figure 101: The Interference Problem
If P
1
is the sound pressure produced by S
1
at point M, and P
2
the pressure produced by S
2
at
point M, the complex sound pressure P
m
resulting from the addition of the two speakers at point
M is calculated as:
If both sources radiate the same pressure P and the real part of the complex sound pressure at
M is considered at time t=t
1
=d
1
/c, the expression simplifies to:
where the path length difference d
2
-d
1
=
δ
d.
From the simplified expression, it is seen that the second source causes a frequency dependent
phase shift given by:
δϑ
= 2
π
f
δ
d/c. When
δϑ
=(2n + 1)
π
, where n=0,1,2,3…= integer,
pressure cancellations occur, since cos(2n +1)
π
= -1.
As a result, pressure cancellation occurs for frequencies that satisfy the condition:
2f
δ
d/c = 2n + 1 where n is an integer.
δ
π
+
=
c
d
f
2
cos
1
P
P
m
e
P
e
P
P
c
d2
t
f
j
2
2
c
d1
t
f
j
2
1
m
−
π
−
π
+
=
Содержание V-DOSC
Страница 1: ...Version 4 June 2005 V DOSC OPERATOR MANUAL ...
Страница 2: ...L ACOUSTICS V DOSC Manual Version 4 6 29 2005 Page 2 of 158 ...
Страница 20: ...L ACOUSTICS V DOSC Manual Version 4 6 29 2005 Page 20 of 158 Figure 6 V DOSC System Block Diagram ...
Страница 21: ...L ACOUSTICS V DOSC Manual Version 4 6 29 2005 Page 21 of 158 Figure 7 Example LR System Configuration ...
Страница 73: ...L ACOUSTICS V DOSC Manual Version 4 6 29 2005 Page 73 of 158 Figure 49 ARRAY 2004 Geometric Data for dV DOSC ...
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Страница 133: ...L ACOUSTICS V DOSC Manual Version 4 6 29 2005 Page 133 of 158 Figure 97 V DOSC Enclosure Line Drawing ...
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