In part 1 of this blog series, we looked at why a clarinet sounded different than a soprano saxophone. Both are “closed” at the mouth piece end and “open” at the end of the bore. Both are identical lengths, yet one functions as a quarter wavelength resonator and has odd numbered multiples of its resonances (clarinet) and the other functions as a one half wavelength resonator (saxophone, and its conical cousins, the oboe and bassoon) with integer multiples of its resonances.
The difference is that the clarinet is a constant diameter cylinder and the saxophone is a conical instrument that gradually gets wider as one gets closer to the bore. The physics is based on the pressure wave, or equivalently, if you want to shift phase, the volume velocity, and it varies according to sin(x) for a cylinder such as a clarinet, but varies according to sin(x)/x for a cone shaped resonator.
Physicists typically talk in terms of “pressure” and audiologists (and speech scientists) talk in terms of “volume velocity”. They are the same thing, but 180 degrees out of phase with each other.
Despite the apparent physical similarity, the clarinet and the soprano saxophone are dramatically different animals and indeed sound quite different: one is a cone and the other is a cylinder. A cone functions as a one half wavelength resonator (F = kv/2L) and a cylinder functions as a one quarter wavelength resonator (F = (2k-1)v/4L).
So,… is the human ear canal a cylinder or a cone?
In audiology textbooks and many pretty pictures we have in our clinics, the ear canal is usually drawn as a cylinder with the ear canal, being “open” at one end and “closed” at the tympanic membrane end. It has its first mode of resonance at 2700 Hz in the adult unoccluded condition. And for those who have real ear measurement systems that can assess up to 10,000 Hz (or for those who have standard clinical real ear measurement systems, and whose patients have a low 2500 Hz resonance), the second mode of resonance is at three times the first one…. So far so good.
This odd numbered multiple is what would be expected from a quarter wavelength resonator cylinder.
But anatomically the ear canal is not a uniform diameter cylinder. There are parts where it is conical and other parts where it is indeed uniform.
It is not unusual for a resonator to have characteristics of all three types of resonators: a quarter wavelength resonator, a half wave length resonator, AND a Helmholtz resonator- one does not obviate the other.
It is also quite possible that the so called “concha related resonance” at about 4500-5500 Hz is not totally a concha or volume related issue, but actually the first mode of resonance of a half wave length resonator (which would be at exactly 2 x 2700 Hz or 5400 Hz). I have touched on this possibility in previous blogs and have written a more complete article on this .
Anyone can perform this simple experiment- take a wad of putty or slightly chewed chewing gum and use it to fill up the concha of a person, then perform a real ear measurement of their unoccluded ear (REUR). Indeed for some people, there will be a high frequency loss of energy (because you deleted the concha resonance) but for others (such as myself), there is no measurable change. If indeed, there is no measurable change and the concha is indeed obstructed, then we are measuring the first mode of resonance of the ear canal where it is functioning as a one half wave length resonator.
If one were to perform this experiment on KEMAR (or simply remove KEMAR’s pinna), there would be a significant high frequency loss. KEMAR uses a cylindrical (Zwislocki coupler) and not one whose shape mimics that of the human ear.
This is not a trivial issue. Many manufacturers have come out with products over the years where either the concha was not occluded in hopes of maintaining the 4500-5500 Hz “unoccluded concha resonance” or placing the hearing aid microphone in that portion of the outer ear in order to pick up some pre-amplified high frequency sound energy.
If indeed this second bump we see on the real ear unaided response (REUR) is related to the earcanal and not the concha, this free pre-amplification may not even be there if the ear canal is occluded in any way.
And as a trivia question- what other FFT spectrum, other than a quarter wavelength resonator, has odd numbered multiples of the primary? (Hint- the magnitude of the higher frequency elements decrease by a factor of 1/f).
