# And The Winner Is….(Part 1)

Whenever I fit hearing protection such as Musicians’ Earplugs, I verify the function using real ear measurement.  Of course, in the design of Musicians’ Earplugs there is a correct assumption that the acoustic gain that is generated will offset the insertion loss caused by the occluding earmold.  That is, if people have a 2700 Hz resonance due their outer ear, in order to achieve a uniform attenuation or flat insertion gain (or loss), one needs to have excess gain generated in the 2700 Hz region because plugging up an ear results in a loss of this natural gain.

Clinically the question arises is, what if the person does not have a 2700 Hz natural resonance but that it is at another frequency?

But let’s take a step back and go over some acoustics – after all, this is only part 1 of this 2-part blog series!

Going back to first year audiology and speech sciences, we have learned that a tube that is “open” on one end and “closed” on the other, functions as a quarter wavelength resonator.  You can verify this with blowing across the top of a straw while pinching the bottom end closed.   The calculated frequency of the resonance of this system is given by F=v/4L where v is the speed of sound and L is the length of the resonating frequency.   And oh yes, there are also resonances at 3 x this frequency, 5 x this frequency, 7 x this frequency, and so on.

In speech sciences the low back unconstricted vowel has its first resonance at 500 Hz (with subsequent ones at 1500 Hz, 2500 Hz, and so on).  Given that the vocal tract is “open” at the lips during the utterance of this vowel and “closed” at the vocal chords, this 500 Hz resonance (which speech scientists call a formant) is a quarter wavelength resonance, and there are odd numbered resonanaces/formants above this.

Using the equation F=v/4L or F= 34,000 cm/sec / 4 x 17 cm, this works out to be 500 Hz (where 34,000 cm/sec is the speed of sound in cm/sec and 17 cm is the length between the vocal chords and the open lips).

Similarly for the human ear canal (just shy of 3 cm in length), its resonance frequency would be F = 34,000 cm/sec / 4 x 3 cm or 2833 Hz.  This is actually a bit higher than the 2700 Hz resonance and the reason lays in the realm of “length” vs. “effective length”.

It turns out that the compliant eardrum is not a brick wall and therefore adds several mm of acoustic length to the calculation. That is, the ear canal behaves as if it is slightly longer than what would be estimated from just taking measurements, such as by x-rays or on cadavers.

This is nothing new – if anyone has ever tried to use the now discontinued Zwislocki coupler in KEMAR for acoustic research, one quickly notices that it is only 21.5 mm long, the remainder 5-8 mm being made up by the compliance of the microphone diaphragm that is used in KEMAR.

But this is taking us adrift of the question at hand: if a person doesn’t have a theoretical 2700 Hz resonance what should we do?

This is seen all of the time; children under the age of 3 have outer ear resonances on the order of 3000-4000 Hz because of their shorter ear canal length and infants may have up to a 7000 Hz resonance. Very large adults with longer than normal ear canals may have a 2400 or 2500 Hz resonance, and then we get into the realm of operated outer ear canals such as Mastoid cavities (with a 1600 Hz resonance).

Two solutions come to mind – do we use the unaltered Musicians’ Earplugs (that “assumes” a 2700 Hz resonance) or do we modify the Musicians’ Earplug dimensions to create a lower frequency resonance that would offset the large adult with a long ear canal, with the net result being a flat insertion loss which provides uniform attenuation across the frequency range of interest?

This would be a really interesting and clinically applicable CAPSTONE project for any AuD doctoral student to undertake.

Of course it’s not so simple – if one alters the dimensions of the Musicians’ Earplugs we can indeed shift the resonance to lower frequency, but alas, there will be a bit of a high frequency roll-off with greater attenuation in the 4000-6000 Hz region than what is typically provided.  (Actually I have a neat way of doing this and controlling for all of the parameters so that each parameter can be looked at separately… so if there are any interested AuD students…)

But, short of doing this study, recently I had a patient who plays both the guitar and percussion who had a 3000 Hz symmetrical notch in their audiogram.  I realize the literature says that for noise induced hearing loss one typically sees a notch in the 3000-6000 Hz region with recovery at 8000 Hz, but clinically I rarely see a 3000 Hz notch- perhaps once a month at most.

This musician also had a 2000 Hz resonant frequency of their outer ear canal and this is consistent with “noise exposure having the greatest effect on frequencies that are about half an octave higher than the offending noise exposure frequency(ies)”.  And indeed, 3000 Hz is roughly half an octave above 2000 Hz which is the frequency of the notch in the audiogram.  He was a neat patient- he was not tall but must have had a 10 foot long ear canal!

So – do I modify the Musicians’ Earplugs to create a 2000 Hz resonance such that the attenuation is perfectly flat up to about 3000 Hz, or do I use unmodified Musicians’ Earplugs that will result in an unfilled-in “notch” at 2000 Hz, but better high frequency acuity?

Stay “tuned” for part 2…

Marshall Chasin, AuD, is a clinical and research audiologist who has a special interest in the prevention of hearing loss for musicians, as well as the treatment of those who have hearing loss. I have other special interests such as clarinet and karate, but those may come out in the blog over time.