I am talking directly into the front of my Samson Q2U, with my lips actually touching the windshield. This is the spectrum plot in Audacity (note the high size):
There is nothing beyond 12000Hz (the sample rate is set at 48000Hz), whereas the advertised frequency response is 50Hz-15000Hz. Does this mean that the microphone is defective?
The spoken human male voice really only has useful frequency content up to about 8kHz usually. This will vary person to person of course, and you could get higher frequency components singing, for example, a strong falsetto. But one shouldn't expect consistent audio information above 8kHz ish for spoken word.
For comparison telephone often has an upper bandwidth of 3.4kHz, far from hi fi but fine for spoken content. A more modern upper bandwidth of about 8kHz is very good quality and will capture pretty much all the useful content of a voice signal.
Very high quality setups for recording music can get closer to 20kHz, theoretically, though many high-end studio staple mics such as the Neumann u87 have a roll off such that the 15khz band is roughly -8dB (that is, 8dB less than the 'flatline' of the bulk of the mics response at audio frequencies). So called reference or measurement microphones such as the DPA 4006A capture 15kHz faithfully. Both of these mentioned mics are around £2000, so we can see that the ability to capture 15kHz is not considered mandatory for recording extremely high quality audio.
To put into perspective, 15kHz is about on the very limit of what I can hear as a 40 year old, and I feel lucky that I can still ALMOST hear this high. It's so high that when using a rising (in frequency) sin and trying to evaluate when it disappears it becomes hard to tell wether you can still hear it or wether it's just an auditory illusion.
So, you shouldn't expect 15kHz from voice apart from the occasional mouth noise or little anomaly, and it's almost always unnecessary to have much content in that area for audio.
On your testing process:
In order to test the manufactures claim that the mic goes up to 15kHz I would advise moving away from human speech and use test tones, steady state sin waves in this case. Repeatable, reliable, tuneable etc. Simply output a few frequencies and see if the spectral response of the mic matches expectation.
Be aware that the loudspeaker will also impart its frequency curve on the audio output. Good studio reference-monitors, specialist speakers with a very flat response for audio work, can produce 15khz easily, and some are claimed to be relatively flat much higher. These are multi speaker solutions with tweeters dedicated solely to producing the high frequency content. These would be preferable for any testing situation.
Using your computer-monitor speakers is not so ideal, as these parts will be (usually) low cost, single speaker solutions just for gaming or watching youtube. Even though it's not that hard to get a speaker producing 15kHz (you just feed it a wave of that frequency and it will oscillate accordingly) the designers would have compromised somewhat to get one driver (ie single speaker) to cover as much of the useful frequency spectrum as possible. Due to the above they are unlikely to feel that reproducing 15kHz is important, and would potentially try and band-limit the speaker so it can work with all it's energy in the useful audio bandwidth. Not to mention things like speaker grills and enclosures prioritised for aesthetic rather than sonic accuracy. Very high frequency audio is delicate, it is readily absorbed or diffused by all manner of surfaces or structures.
For this reason I don't see it as much of an indicator of mic performance that the test tone is picked up less as the frequency gets higher. The fact the speaker produces it, and the mic clearly picks up some of it would usually be considered a pretty good result in a simple test. Even if the mic is in fact a few dB less at 15kHz, and the manufacturers were being a little optimistic with the reports, then the fact it still seems to pick up some 15kHz is no problem at all, it's working in that area, if you need more you can easily boost.
But that aside, I think the computer-monitor speaker outputting quieter at 15kHz is much more likely.
Anyway, by probing your system, outputting various frequencies you can build up a picture of whats going on, though it may not tell you a huge amount about what the mic is actually doing without a very flat, high quality speaker.
In doing so you will see many values quoted in dB. It should be noted that dB is a relative scale, not absolute (unless you are using dB"sound pressure level" which gives a dB value in reference to 0dBspl, defined as the quietest sound a human can hear. Useful for safety measurements but often useless when testing gear or mixing audio).
So a device outputting -5dB usually means -5dBfs where fs = full scale, which means the maximum value a signal can take as it's used in the software, calibrated usually to the physical output capabilities of the device via the DAC audio-device's driver.
Other dB implementations, such as dBv or dBu are more useful for analog circuits that don't have a definite cutoff (clipping) point but I won't go into that here.
Once your -5dBfs signal is converted to analog the amplifier for your computer speakers can then attenuate or boost this and the -5dBfs value becomes meaningless. At this point it's only really measurable in dBspl, and can be quiet to loud depending on the volume settings of your speakers' amp. The mic then picks it up, applies its own gain, then converts to digital. The dBfs rating given by the spectrum analyser is saying 'in comparison to the AD converter's maximum allowable input at that frequency' (which would usually be very flat across the spectrum). As such, a dBfs measurement in the source system compared to one in the destination system are relatively unrelated, unless you have calibrated the speaker volume to make it so, and this may not be possible for every amp/speaker combo (ie. you may not be able to get a computer speaker loud enough to get close to the eg. -5dBfs in the mic).
In general the typical software dB readings are only useful to check you are not overloading (distortion, which causes non-linearities), or to compare signals in one 'node' of an audio system, be it a mixer in a DAW or used in comparative analysis at a point of capture. In other words, don't worry about the sig gen app's dBfs out compared to the received signals dBfs in, it's enough to just look at relative relationships over the received frequency spectrum.
You could get into how WELL, ie how faithfully the mic output is a copy of the mic input but well, thats REALLY getting into very high end, subjective, very hard to pin down or prove, stuff. Even pinning down where any distortion is coming from would be hard enough, and it's not a source of worry for audio recording when expensive legendary mics are happy to drop -8dB at 15kHz by design.
All in all the main thing often comes down to 'does it sound good?' and your test recording sounds absolutely fine to me for a good quality entry level mic. It captures everything needed in the spoken voice and you have endless opportunity to process it further.
All of this pertains to the analog side of your mic. We can be pretty sure that THAT is working ok. I understand there are irregularities in frequency response in this mic when using different USB sockets, but that is much more to do with the USB protocol and how signal transfer is negotiated. Investigating that would be a lot harder, but as it is ok in some circumstances it's probably more an environment issue rather than an issue with the mic's ADC, as this can be shown to work correctly with particular setups. It MAY be to do with mic firmware, usb versions or computer handshake protocols. I would suggest that as it works ok in some cases you treat it more like a versioning problem that you have to accommodate for, rather than an error with the mic. The mic can output analog audio via XLR if necessary so if this proves a problem you can always use an interface for the conversion down the line.
Finally, your post processing sounds perfectly fine, too, for speech! How it's delivered is a matter of preference, I enjoy slightly more bias towards the lower end which makes longer listening sessions easier and gives the voice a bit more weight but many like the sort of sound you have, and I have heard much worse quality on big name educational courses. You may like to use (or use a bit more) compression but again that is a matter of taste.
