Are loudspeaker diaphragms acoustically transparent?

[thadman]

I'm in a bit of a dilemma, I'm not sure whether or not loudspeaker diaphragms are acoustically transparent or the degree to which it effects their motion.

A few ideas,

Below the fundamental mode of the enclosure, the air behaves with a single phase. The acoustic forces (and their effects on diaphragm motion) within the enclosure could be described accurately by the air compliance.

Within the modal region of the enclosure, the air has a multi-dimensional phase property, however Ray acoustics still do not apply. The acoustic forces (and their effects on diaphragm motion) within the enclosure could be described accurately by analyzing the modal surface encompassing the diaphragm.

Above the Schroeder frequency of the enclosure, we'll assume Ray acoustics apply. In this region, acoustic waves should be propagating through the enclosure space (ie reflections will be present due to the impedance mismatch between the air and enclosure walls/diaphragm). It is over this bandwidth that the effects of the acoustic transparency of the diaphragm have me curious.

At the interface between two dissimilar masses, an impedance mismatch is found. This is the reason we observe reflections.

Above the Schroeder frequency, reflections are believed to occur. If we assume a reflection occurs, we must also assume the presence of an impedance mismatch.

Let's assume we have two masses (Mass A = air, Mass B = loudspeaker diaphragm). We assume a propagating wave (Mass A --> Mass B) contacts the interface between the two masses. At the interface we observe a reflection (wave is reflected back to Mass A), however some of the energy is absorbed by Mass B.

Wouldn't this dictate that propagating waves have an influence on diaphragm motion due to the impedance match (ie 100% reflections are not observed) and we must thus consider their influence if we wish to accurately simulate a loudspeaker system?

Over what bandwidths should the impedance match be considered?

If any of my assumptions are inaccurate or incomplete, I would much appreciate some feedback.

Thanks,
Thadman

 

[famousken]

I like to think of them as being acoustically conductive. If a sound is hitting the back of the speaker cone, it is most definatlly going to be heard on the front of the driver, but I wouldn't call them transparent because otherwise they wouldn't be vary efficient at creating sound (not that they are anyways). Think about it this way, they are designed to produce sound from mechanical vibrations, it doesn't matter if those vibrations come from a secondary source at their back or form their motor, the speaker is going to turn those vibrations into sound at their front. This is the reason designers spend so much time designing speaker boxes that minimize reverberation.

 

[Bob S]

Hello Thadman-
I am not a professional acoustical engineer, so here are my guesses.
1) A disconnected loudspeaker has a natural resonant frequency, the restoring force due to the stiffness in the cone. This is like Hooke's Law; F = kx, where F is the restoring force and k is the spring constant. If the cone has a mass M. then the resonant frequency would be sqrt(k/M) in radians per second.
2) A connected speaker with the amplifier turned on can have a different resonant frequency depending on wheather the amplifier output is a voltage source or a current source. A power pentode (e.g., EL-34) is a current source, and an npn transistor emitter (e.g., 2N3055) is a voltage source. The current source will let the cone resonate at the natural frequency. The voltage source will change the resonant frequency, because the moving speaker coil in a magnetic field will generate back emf currents.
Bob S

 

[neurosport]

well of course some of the sound will pass out of the cabinet through the speaker - but what does that mean ?

all it means is that some time offset signal will mix with the original perhaps producing deviations in response on the order of one tenth of a single decibel.

considering the speaker itself may have irregularities of as much as 20 decibel i don't think that would be significant.

now if you build a pipe-like enclosure that provides acoustical loading for the back of the speaker this can maximize the energy transfer to the volume of air in the speaker, then if you happen to place the speaker at a pressure maximum on a resonance mode you may have significant effects ...