I am currently modelling an acoustic planar wave, generated by a speaker, travelling through an expanding cross sectional area duct/horn system. When plotting a graph of transmission coefficient against frequency, the model suggests the transmission coefficient is between 0.5 and 1 for all frequencies. Should transmission coefficient, defined as the ratio of output to input amplitude, have a transmission coefficient above one, or do my results seem feasible?
Note, the medium through which the wave propagates is constant (air).
The total power (intensity times area) over the cross section should remain constant, so the amplitude should not get larger as the cross-section increases. The amplitude is proportional to the square root of intensity so should be proportional to 1/sqrt(area) if the wave has uniform intensity all the way across the duct cross-section. The transmission coefficient could be larger than 1 if the duct area reduced.
No. it is likely that some bass will not enter the hole. The correction is described by Sewell.
Sound is not water progressing in a pipe... You have to bring into your picture the notion of impedance matching between your sound source (the speaker membrane moved by a linear electromagnetic driver) and the medium (air in open field). The horn contributes to reduce the impedance gap hence increases the radiation effectiveness of the speaker - this is true only in a limited frequency band where the extent of the membrane is a fraction of the acoustic wavelength (every one knows you need bigger loudspeakers for lower frequencies). With a poor impedance matching only a mere fraction of the mechanical power will turn into acoustic power. This means that, for the same electro-mechanical driving force (or membrane velocity), you will increase the SPL in the open space by inserting your horn thanks to the better impedance matching, without contradicting the principle of energy conservation. This is what you have seen maybe - depending of the choice of "input" defining your global "transmission coefficient". As rightly commented by Anders, the impedance mismatch at any step of an "acoustic path" acts as a partial reflector: when the impedance matching is poor, the electromagnetic driver of the loudspeaker is unable to deliver "active power" in the open field. You can separate active and reactive power indirectly by measuring the out-phasing between tension and current in the coil (but you have to factor the Joule effect), or directly by measuring the sound intensity (e.g. from the pressure gradient https://en.wikipedia.org/wiki/Sound_intensity) anywhere along the acoustic path...
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