The Minnaert resonance is the acoustic resonance frequency of a single bubble in an infinite domain of water (neglecting the effects of surface tension and viscous attenuation). The resonant frequency is given by
f
=
1
2
π
a
(
3
γ
p
A
ρ
)
1
/
2
where
a
is the radius of the bubble,
γ
is the polytropic coefficient,
p
A
is the ambient pressure, and
ρ
is the density of water. This formula can also be used to find the resonant frequency of a bubble cloud with
a
as the radius of the cloud and
ρ
the difference between the density of water and the bulk density of the cloud. For a bubble in water at standard pressure
(
p
A
=
100
k
P
a
,
ρ
=
1000
k
g
/
m
3
)
, this equation reduces to
f
a
≈
3.26
m
/
s
, where
f
is the resonant frequency of the bubble.
