With the nonlinear response of typical electrical-to-acoustic transducers, what methods are available to characterize their nonlinear behaviour to test signals other than pure tones? I am specifically thinking about insert earphones for audiometry. In particular, the Etymotic ER2 and ER3 earphones (see Etymotic transducers).
I have the frequency-magnitude response from the manufacturer for these two devices, but these characterize the response of each transducer at discrete tones across a range of frequencies that typically extends from 20 Hz to 20 kHz. It only offers the magnitude response and does not provide any other information.
A colleague suggested the following method to elicit some insight into the response of these devices to more complex electrical signals like tone bursts and chirps. Using two pure tones, fix one tone at a low frequency and set the second tone just on the lower side of 20 kHz. With the large frequency separation, it would seem logical that there would be no interaction between the two tones. As the higher frequency tone is moved towards the fixed lower frequency tone, more interaction between the tones would be expected. This is a unique approach and could provide more information about the response of each transducer, but is still limited.
Any suggestions are welcomed.
I'm not sure I get your "point". You seem to describe an ordinary audio speaker, whose construction has innumerable forms. If what you ask is about audio speakers, then there's an entire field of engineering devoted to this, so maybe you should start there. A lot of high-end audio equipment is devoted to phase linear response as being the closest to "pure fidelity".
Back in the mid-70s, I worked at a Burstein-Applebee (BA) hifi store while going to college (both were full time). From that, I recall that Panasonic/Technics heavily promoted their phase linear speakers, while the Ohm G speaker cones were layered with (4?) different materials for optimal frequency response flatness (I don't think they referenced phase at all). My early work with speakers taught me that a speaker by itself is nothing without a well designed box. A speaker's electroacoustic measurements only a starting place for a good enclosure design. There are all sorts of enclosure design types: passive radiator, horn, folded horn, tuned-port, bass reflex, etc. Horn designs were typically exponential or even hypergeometric to "flatten" frequency response, much like a horn antenna's wider frequency response.
There's also transient response (TIM) and a host of other audio properties, but most seemed to be selling points, albeit good sounding ones. At night, the assistant BA store manager and some of us would hook up banks of amplifiers and speakers for our own listening tests. Sometimes we had to explain to the police responding to calls by upset residential neighbors that we were checking new equipment and that we "didn't notice it was so late already". One of the favorite test "songs" was Tchaikovsky's 1812 Overture (on LP vinyl of course), with it's great cannon blasts (some versions were much better than others), but there was also the usual Pink Floyd, Yes, Queen, Jethro Tull, etc. These really stress tested super audio equipment (think acoustic feedback on a lousy turntable!). The entire signal chain has to be good, or even the best speaker sounds bad.
Now, without real details as to the "problem" you want to solve, the query space is much too vast to even begin an analysis. We don't even know the name of the transducer.
When I was in college, I took a course in the physics of sound. We were taught that the exponential shape of the horn had more to do with the polar pattern, dispersing the sound over a wider angle. I haven’t conducted any experiments to verify, but thought it was worth mentioning
I am a research engineer into loudspeakers. If by non-linearity you are concerned with harmonic and inter-modulation distortion, the frequency magnitude response per se tells us practically nothing about this. Using frequencies of 20 Hz and 20 KHz is not a good idea, as 20 Hz will probably drive vented enclosures below the tuned frequency of the vent and enclosure, causing very large cone displacements and harmonic distortion from the low frequency driver only. In order to identify the non-linearity of a loudspeaker that uses a crossover network, it needs to be swept from fb to fh, with a synchronous filter that either notches out f, or is tuned to 2f, 3f, 4f,...etc. to identify its harmonic distortion.
Loudspeaker drivers tend to suffer from breakup modes at specific frequencies. Such breakup modes can be very non-linear indeed, giving a 'bum note' at those frequencies.
You mention the phase of a loudspeaker: We must bear in mind that phase is derived from the impulse response and that it is in the context of frequencies that are continuous, i.e. that have lasted forever. Heyser[1-4] showed that a loudspeaker is frequency-dispersive, and that its phase just is what it is. The phase of a loudspeaker can cause a loudspeaker to appear to be minimum phase, linear phase or even zero phase, but the time-frequency performance of a loudspeaker is much more complicated.
Loudspeaker Phase Characteristics and Time Delay Distortion: Part 1
Richard C. HeyserJ.A.E.S., Vol 17 P. 30-41 (January 1969)
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Loudspeaker Phase Characteristics and Time Delay Distortion: Part 2
Richard C. HeyserJ.A.E.S., Vol 17 P. 130-137 (April 1969)
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Determination of Loudspeaker Signal Arrival Times Part 1
Richard C. HeyserJ.A.E.S, Vol 19 P. 734-743 (October 1971)
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Determination of Loudspeaker Signal Arrival Times Part 2
Richard C. HeyserJ.A.E.S., Vol 19 P. 829-834 (November 1971)