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Formula Sheet
RMS
Sine
Wave:
d
B
R
M
S
=
x
d
B
p
2
,
where
d
B
p
=
decibels
peak
\text{Sine } \allowbreak \text{Wave: } dB_{RMS} =\frac{x\ dB_{p}}{\sqrt{2}}\text{, } \allowbreak \text{where } dB_{p} =\text{decibels } \allowbreak \text{peak}
Sine
Wave:
d
B
RMS
=
2
x
d
B
p
,
where
d
B
p
=
decibels
peak
Frequency
f
=
1
T
,
where
f
=
frequency
and
T
=
period
f=\frac{1}{T}\text{ , } \allowbreak \text{where } f=\text{frequency } \allowbreak \text{and } T=\text{period}
f
=
T
1
,
where
f
=
frequency
and
T
=
period
f
=
ν
λ
,
where
f
=
frequency,
ν
=
wave
speed,
and
λ
=
wavelength
f=\frac{\nu }{\lambda }\text{, } \allowbreak \text{where } f=\text{frequency, } \nu =\text{wave } \allowbreak \text{speed, } \allowbreak \text{and } \lambda =\text{wavelength}
f
=
λ
ν
,
where
f
=
frequency,
ν
=
wave
speed,
and
λ
=
wavelength
Wavelength
λ
=
ν
f
,
where
f
=
frequency,
ν
=
wave
speed,
and
λ
=
wavelength
\lambda =\frac{\nu }{f}\text{ , } \allowbreak \text{where } f=\text{frequency, } \nu =\text{wave } \allowbreak \text{speed, } \allowbreak \text{and } \lambda =\text{wavelength}
λ
=
f
ν
,
where
f
=
frequency,
ν
=
wave
speed,
and
λ
=
wavelength
Distance
d
=
r
t
,
where
d
=
distance,
r
=
rate,
t
=
time
d=rt\text{ , } \allowbreak \text{where } d=\text{distance, } r=\text{rate, } t=\text{time } \allowbreak \text{}
d
=
r
t
,
where
d
=
distance,
r
=
rate,
t
=
time
Time
t
=
d
r
,
where
d
=
distance,
r
=
rate,
t
=
time
(To
get
m
s
from
s
e
c
o
n
d
s
multiply
by
1000
)
t=\frac{d}{r}\text{ , } \allowbreak \text{where } d=\text{distance, } r=\text{rate, } t=\text{time } \allowbreak \text{(To } \allowbreak \text{get } ms\text{ from } seconds\text{ multiply } \allowbreak \text{by } 1000\text{)}
t
=
r
d
,
where
d
=
distance,
r
=
rate,
t
=
time
(To
get
m
s
from
seco
n
d
s
multiply
by
1000
)
Thresholds
Pascals
20
μ
P
a
or
20
×
1
0
−
6
P
a
20\micro Pa\text{ or } 20\times 10^{-6} \ Pa
20
μ
P
a
or
20
×
1
0
−
6
P
a
Dynes
.
0002
d
y
n
e
s
c
m
2
.0002\ \frac{dynes}{cm^{2}}
.0002
c
m
2
d
y
n
es
Recall
since
these
are
the
same
threshold
we
can
say
they
are
equal
thus:
\text{Recall } \allowbreak \text{since } \allowbreak \text{these } \allowbreak \text{are } \allowbreak \text{the } \allowbreak \text{same } \allowbreak \text{threshold } \allowbreak \text{we } \allowbreak \text{can } \allowbreak \text{say } \allowbreak \text{they } \allowbreak \text{are } \allowbreak \text{equal } \allowbreak \text{thus:}
Recall
since
these
are
the
same
threshold
we
can
say
they
are
equal
thus:
.
00002
P
a
.
0002
d
y
n
e
s
c
m
2
=
1
=
.
1
P
a
d
y
n
e
s
c
m
2
\frac{.00002\ Pa}{.0002\ \frac{dynes}{cm^{2}}} =1=.1\frac{Pa}{\frac{dynes}{cm^{2}}}
.0002
c
m
2
d
y
n
es
.00002
P
a
=
1
=
.1
c
m
2
d
y
n
es
P
a
Sound Power
1
0
−
12
W
m
2
\frac{10^{-12} \ W}{m^{2}}
m
2
1
0
−
12
W
deciBells
dB
SPL
(Sound Pressure Levels)
d
B
S
P
L
=
20
log
(
x
m
e
a
s
u
r
e
d
x
r
e
f
)
dB_{SPL} =20\log\left(\frac{x_{measured}}{x_{ref}}\right)
d
B
SP
L
=
20
lo
g
(
x
re
f
x
m
e
a
s
u
re
d
)
dB
SP
(Sound Power)
d
B
S
P
=
10
log
(
x
m
e
a
s
u
r
e
d
x
r
e
f
)
dB_{SP} =10\log\left(\frac{x_{measured}}{x_{ref}}\right)
d
B
SP
=
10
lo
g
(
x
re
f
x
m
e
a
s
u
re
d
)
Uncorrelated Sound
T
o
t
a
l
d
B
=
10
log
(
1
0
x
1
d
B
S
P
L
10
+
1
0
x
2
d
B
S
P
L
10
+
.
.
.
+
1
0
x
n
d
B
S
P
L
10
)
Total\ dB\ =\ 10\ \log\left( 10^{\frac{x_{1} \ dB\ SPL}{10}} +10^{\frac{x_{2} \ dB\ SPL}{10}} +...+10^{\frac{x_{n} \ dB\ SPL}{10}}\right)
T
o
t
a
l
d
B
=
10
lo
g
(
1
0
10
x
1
d
B
SP
L
+
1
0
10
x
2
d
B
SP
L
+
...
+
1
0
10
x
n
d
B
SP
L
)
Correlated Sound
T
o
t
a
l
d
B
=
20
log
(
1
0
x
1
d
B
S
P
L
20
+
1
0
x
2
d
B
S
P
L
20
+
.
.
.
+
1
0
x
n
d
B
S
P
L
20
)
Total\ dB\ =\ 20\ \log\left( 10^{\frac{x_{1} \ dB\ SPL}{20}} +10^{\frac{x_{2} \ dB\ SPL}{20}} +...+10^{\frac{x_{n} \ dB\ SPL}{20}}\right)
T
o
t
a
l
d
B
=
20
lo
g
(
1
0
20
x
1
d
B
SP
L
+
1
0
20
x
2
d
B
SP
L
+
...
+
1
0
20
x
n
d
B
SP
L
)
Pressure Total
T
o
t
a
l
d
B
S
P
L
=
10
log
(
p
1
2
+
p
2
2
+
.
.
.
+
p
n
2
p
0
2
)
Total\ dB_{SPL} =10\log\left(\frac{p_{1}^{2} +p_{2}^{2} +...+p_{n}^{2}}{p_{0}^{2}}\right)
T
o
t
a
l
d
B
SP
L
=
10
lo
g
(
p
0
2
p
1
2
+
p
2
2
+
...
+
p
n
2
)
where:
p
is
a
pressure
and
p
0
is
its
reference
pressure.
\text{where: } p\text{ is } \allowbreak \text{a } \allowbreak \text{pressure } \allowbreak \text{and } p_{0}\text{ is } \allowbreak \text{its } \allowbreak \text{reference } \allowbreak \text{pressure. } \allowbreak \text{}
where:
p
is
a
pressure
and
p
0
is
its
reference
pressure.
Sound at a Distance
T
o
t
a
l
d
B
S
P
L
=
C
o
n
s
t
d
B
S
P
L
−
20
log
(
D
o
b
s
e
r
v
e
d
D
r
e
f
)
Total\ dB_{SPL} =Const\ dB_{SPL} -20\log\left(\frac{D_{observed}}{D_{ref}}\right)
T
o
t
a
l
d
B
SP
L
=
C
o
n
s
t
d
B
SP
L
−
20
lo
g
(
D
re
f
D
o
b
ser
v
e
d
)
Reflected Sound
R
e
f
l
e
c
t
i
o
n
d
B
S
P
L
a
t
l
i
s
t
e
n
i
n
g
p
o
s
i
t
i
o
n
=
20
log
(
D
i
r
e
c
t
P
a
t
h
l
e
n
g
t
h
R
e
f
l
e
c
t
e
d
P
a
t
h
l
e
n
g
t
h
)
Reflection\ dB_{SPL} \ at\ listening\ position\ =\ 20\log\left(\frac{Direct\ Path\ length}{Reflected\ Path\ length}\right)
R
e
f
l
ec
t
i
o
n
d
B
SP
L
a
t
l
i
s
t
e
nin
g
p
os
i
t
i
o
n
=
20
lo
g
(
R
e
f
l
ec
t
e
d
P
a
t
h
l
e
n
g
t
h
D
i
rec
t
P
a
t
h
l
e
n
g
t
h
)
Assumes
inverse
square
propagation.
Note
this
formula
gives
the
decrease
in
level.
\text{Assumes } \allowbreak \text{inverse } \allowbreak \text{square } \allowbreak \text{propagation. } \allowbreak \text{Note } \allowbreak \text{this } \allowbreak \text{formula } \allowbreak \text{gives } \allowbreak \text{the } \allowbreak \text{decrease } \allowbreak \text{in } \allowbreak \text{level.}
Assumes
inverse
square
propagation.
Note
this
formula
gives
the
decrease
in
level.
Delay
Reflected delay
R
e
f
l
e
c
t
i
o
n
d
e
l
a
y
=
(
R
e
f
l
e
c
t
e
d
p
a
t
h
l
e
n
g
t
h
)
−
(
D
i
r
e
c
t
p
a
t
h
l
e
n
g
t
h
)
ν
Reflection\ delay\ =\ \frac{( Reflected\ path\ length) \ -\ ( Direct\ path\ length)}{\nu }
R
e
f
l
ec
t
i
o
n
d
e
l
a
y
=
ν
(
R
e
f
l
ec
t
e
d
p
a
t
h
l
e
n
g
t
h
)
−
(
D
i
rec
t
p
a
t
h
l
e
n
g
t
h
)
Where
ν
is
the
speed
of
sound,
assumes
a
completely
reflective
surface.
\text{Where } \nu \text{ is } \allowbreak \text{the } \allowbreak \text{speed } \allowbreak \text{of } \allowbreak \text{sound, } \allowbreak \text{assumes } \allowbreak \text{a } \allowbreak \text{completely } \allowbreak \text{reflective } \allowbreak \text{surface. } \allowbreak \text{}
Where
ν
is
the
speed
of
sound,
assumes
a
completely
reflective
surface.
Diffusion
Lowest Frequency Diffused
f
=
1130
4
D
f=\frac{1130}{4D}
f
=
4
D
1130
Where
f
=
frequency,
and
D
=
depth
\text{Where } f=\text{frequency, } \allowbreak \text{and } D=\text{depth}
Where
f
=
frequency,
and
D
=
depth
Room Modes
For Axial
f
=
565
L
or
f
=
ν
2
D
f=\frac{565}{L}\text{ or } f=\frac{\nu }{2D}
f
=
L
565
or
f
=
2
D
ν
Where
L
=
dimension
of
interest,
v
=
speed
of
sound,
and
D
=
distance
between
walls
\text{Where } L=\text{dimension } \allowbreak \text{of } \allowbreak \text{interest, } v=\text{speed } \allowbreak \text{of } \allowbreak \text{sound, } \allowbreak \text{and } D=\text{distance } \allowbreak \text{between } \allowbreak \text{walls}
Where
L
=
dimension
of
interest,
v
=
speed
of
sound,
and
D
=
distance
between
walls
General Formula
f
=
c
2
p
2
L
2
+
q
2
W
2
+
r
2
H
2
f=\frac{c}{2}\sqrt{\frac{p^{2}}{L^{2}} +\frac{q^{2}}{W^{2}} +\frac{r^{2}}{H^{2}}}
f
=
2
c
L
2
p
2
+
W
2
q
2
+
H
2
r
2
Where
\text{Where}
Where
p
,
q
and
r
are
room
mode
numbers
(always
integers)
p,\ q\text{ and } r\text{ are } \allowbreak \text{room } \allowbreak \text{mode } \allowbreak \text{numbers } \allowbreak \text{(always } \allowbreak \text{integers)}
p
,
q
and
r
are
room
mode
numbers
(always
integers)
L
,
W
and
H
are
dimensions
of
the
room
L,\ W\text{ and } H\text{ are } \allowbreak \text{dimensions } \allowbreak \text{of } \allowbreak \text{the } \allowbreak \text{room}
L
,
W
and
H
are
dimensions
of
the
room
c
is
the
speed
of
sound.
c\text{ is } \allowbreak \text{the } \allowbreak \text{speed } \allowbreak \text{of } \allowbreak \text{sound. } \allowbreak \text{}
c
is
the
speed
of
sound.
Absorption
A
=
S
a
A=Sa
A
=
S
a
Where
A
=
total
absorption
in
Sabines,
S
=
surface
area,
a
=
absorption
coefficient
\text{Where } A=\text{total } \allowbreak \text{absorption } \allowbreak \text{in } \allowbreak \text{Sabines, } S=\text{surface } \allowbreak \text{area, } a=\text{absorption } \allowbreak \text{coefficient } \allowbreak \text{}
Where
A
=
total
absorption
in
Sabines,
S
=
surface
area,
a
=
absorption
coefficient
Reverb Time
R
T
60
=
V
(
0.049
)
A
t
o
t
a
l
RT_{60} =\frac{V( 0.049)}{A_{total}}
R
T
60
=
A
t
o
t
a
l
V
(
0.049
)
Where
V
=
volume,
A
t
o
t
a
l
=
total
absorption
in
Sabines.
\text{Where } V=\text{volume, } A_{total} =\text{total } \allowbreak \text{absorption } \allowbreak \text{in } \allowbreak \text{Sabines.}
Where
V
=
volume,
A
t
o
t
a
l
=
total
absorption
in
Sabines.
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