You are intent on circling back around to human anatomy. I agree that anatomy is important. I will also say that anatomy is largely variable. Even if we use a standard fake ear it will add peaks and dips to our high frequency measurements that will confuse the measurement and comparison of the headphone hardware. There is much to measure prior to adding 39 types of ear into the mix.
Well, then let's just agree that we have different philosophies about headphone measurement.
I think that everything up to this point has been sufficiently elaborated. The reader and operator shall decide which route to follow.
This is the definition of “Pressure-field” not Diffuse-Field.
My definition of a pressure field configuration is a microphone being flush mounted with a boundary layer which exposes the diaphragm of a pressure microphone (omni) to a 180° sound field.
Here is the definition shared by GRAS:
A pressure microphone is for measuring the actual sound pressure on the surface of the microphone’s diaphragm. A typical application is in the measurement of sound pressure in a closed coupler [here: ear simulators] or the measurement of sound pressure at a boundary or wall [here: flat plate rig]; in which case the microphone forms part of the wall and measures the sound pressure on the wall itself.
Side note: The flush mounted variant is also being referenced as "Boundary Layer Microphone" (BLM) and should not be confused with Crown's concept of the "Pressure Zone Microphone" (PZM) which is a 90° configuration applied
onto the surface instead of flush mounting
into the surface.
One place where you and I appear to have a completely different view is if headphones operate in a Diffuse-Field or Pressure-field.
[...]
“Pressure-field” SPL measurements are much less dependent on external ear anatomy than Diffuse-Field measurements.
A diffuse field mic configuration where the capsule is exposed to theoretically 360° of sound has nothing to do with headphone measurement per se. As already mentioned, I am talking about pressure field configurations where the mic is mounted flush into the surface or into an ear simulator.
All of that does not mean that there cannot be
diffuse sound incuded by reflections inside of the ear cup, though. That was the point I was refering to considering the pressure add up in front of the capsule for the 0° incidence versus "random incidence" up to +/- 90°.
Admittedly, I have to correct one aspect:
The pressure add up increasing the
higher frequency response does only apply for a mic in the free field. As soon as the mic is mounted flush into the boundary the critical frequency is lowered due to the increase of the boundary layer's surface which acts like an enlargement of the front of the capsule.
Pressure doubling formula:
f = c / d
For a 10 mm capsule that would be around 34.3 kHz for the full wavelength and around 8.6 kHz for the 1/4 wavelength.
If we now increase the area to say 100 mm we would end up with 3,4 kHz (full) and 857 Hz (1/4). A 150 mm plate would end up with 2,3 kHz (full) and 572 Hz (1/4). And so on ...
The formula is expecting +3 dB for the 1/4 wavelength and +6 dB for the full wavelength in a 0° incidence where the incomming and the reflected wave overlap with each other. In theory, everything above the calculated frequency would be boosted by up to 6 dB. In some cases (without proper damping of the front grid) the effect is said to take even up to 10 dB initially and then drop to 6 dB calculated above.
I am not sure by how much this effect has to be addressed with the larger surfaces in a headphone measurement situation. I assume that it largely depends on the directivity of the excited sound field where a lot of on-axis (0° +/- a few) resonance could raise the level up from the calculated frequency whereas a lot of off-axis (diffuse sound field up to +/- 90° on a flat plate) might mask the effect. On the other hand, headphone drivers are not working as point sources and add a lot of foam on the side damping such resonances. So there might be different rules for this specific case.
Maybe our colleague
@Mad_Economist has any info on that topic for headphone measurement situations on flat plate rigs?