I'm missing commenting people but I have a good excuse - my computer is pretty much dead, and doesn't stay on long enough for me to do anything. Apparently there's a lecture in here. gtg! x
Imagine a plane acoustic wave propagating in a semi-infinite duct. The duct termination impedance is Z and impedance of air inside the duct is Z0. Due to the impedance discontinuity at x=0 part of the acoustic energy will be transmitted out of the duct, another part will be reflected back into the duct. The total field in the duct is the superposition of incident and reflected waves. At any point x<0 inside the duct, the acoustic pressure can be mathematically represented as a ( ) j ( t kx) r j t kx i r i p p p Pe P e − + = + = + w w . (1) Amplitudes of the reflected and incident waves are related as r i P = RP , where 0 0 Z Z Z Z R + − = is pressure reflection coefficient of the duct termination. Let’s first consider perfect standing waves which appear if duct is terminated by a rigid wall or by a pressure release boundary. In this case no energy will be transmitted out of the duct, everything will be reflected.
OK so those equations come out totally wrong but still, :'(!
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termination impedance is Z and impedance of air inside the duct is Z0. Due to the
impedance discontinuity at x=0 part of the acoustic energy will be transmitted out of
the duct, another part will be reflected back into the duct. The total field in the duct is
the superposition of incident and reflected waves. At any point x<0 inside the duct,
the acoustic pressure can be mathematically represented as a
( ) j ( t kx)
r
j t kx
i r i p p p Pe P e − + = + = + w w . (1)
Amplitudes of the reflected and incident waves are related as r i P = RP , where
0
0
Z Z
Z Z
R
+
−
= is pressure reflection coefficient of the duct termination.
Let’s first consider perfect standing waves which appear if duct is terminated by a
rigid wall or by a pressure release boundary. In this case no energy will be transmitted
out of the duct, everything will be reflected.
OK so those equations come out totally wrong but still, :'(!
Reply
Reply
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