Biomedical Engineering Reference
In-Depth Information
ae
ikL
+
be
−ikL
=0
,
(2.31)
a
−
b
=
u
0
.
(2.32)
cρ
0
With these coe
cients, it is possible to compute the pressure and, therefore,
the velocity at the end. The latter has an oscillation amplitude
u
cos(
kL
)
.
v
x
=
L
=
(2.33)
The divergence at the resonances reflects the idealization of neglecting
dissipation. However, it clearly conveys the idea that for some frequencies
(those that correspond to
ω
n
=
ck
n
=
c
(2
n
+1)
π/
(2
L
)), the particle velocity
at the open end will be maximum. Owing to these velocity fluctuations at
the open end, there will be variations of the flux that, as discussed at the
begining of the chapter, constitute the source of the emitted sound.
