20Q: Acoustics 101 with a Dash of 201

From the Desk of Gus Mueller

I’m remembering an article from The Hearing Journal from about 25 years ago, when CIC hearing aids were becoming popular. In those days, the CIC product filled the ear canal, and there was little room for venting, so the own-voice occlusion effect was a huge problem. In the article, the author pointed out the magnitude of the problem using a diagram showing a potential hearing aid occlusion effect of 25 dB (this indeed is possible) for a patient who also had 25 dB of hearing aid gain for the same frequency region. He concluded that this hypothetical patient, who only had a moderate loss, now had 50 dB of gain for the low frequencies. Not good. Except...when you add dB you find that 25 + 25 = 28, not 50!  Knowledge of acoustics can be helpful in making clinical decisions.

Have you ever had a patient, who after being fitted with new hearing aids, tells you that when he went out to a restaurant, the people from a table away from him were louder than the people at his own table? This of course is impossible, unless the SPL from the people at the other table really was greater than the voices at his own table at his ear. Knowledge of acoustics can be helpful for patient counseling.

And, acoustics also can be fun. What audiologist didn’t enjoy the Myth Busters TV episodes when they went out in search of a “Brown Tone,” when they tried to determine if the human voice can shatter a crystal wine glass, or when they set out to answer the age-old question, “Does a duck’s quack echo?”

When we think of the combination of acoustics, clinical savvy, and fun, one name comes to mind—Marshall Chasin, AuD, who is our guest author this month at 20Q.  Marshall is the Director of Auditory Research at the Musicians' Clinics of Canada, Adjunct Professor at the University of Toronto, Associate Professor in the School of Communication Disorders and Sciences at the Western University, and Adjunct Research Assistant Professor at the State University of New York at Buffalo.                              

You are probably familiar with at least one or two of Marshall's eight books—the classic being Musicians and the Prevention of Hearing Loss, published in 1996. You’ve probably also enjoyed reading many of his monthly columns at the Hearing Review or visiting his weekly blog at Hearing Health Matters (where you can also check out his new e-book, Music to Your Ears).

Marshall doesn’t seem to be slowing down, as he recently developed a new smartphone app to determine if temporary threshold shift (TTS) has occurred during a potential noise-hazardous event. It’s called Temporary Hearing Loss Test app, available at your neighborhood app store. And always, you’ll find Marshall’s work informative, intriguing, and a bit entertaining, too. This 20Q article is no exception.

Gus Mueller, PhD
Contributing Editor
May 2017

Browse the complete collection of 20Q with Gus Mueller CEU articles at www.audiologyonline.com/20Q

20Q: Acoustics 101 with a Dash of 201

 Marshall Chasin, AuD 

1. My audiology training program was not very strong in acoustics.  How did you come about being an expert?
I’m not so sure that I’m an expert, but I do find acoustics, especially clinically relevant acoustics, an interesting topic to write about.  My background was in mathematics (and a prior masters in linguistics). Even so, my first real brush with clinical acoustics was reading an excellent 1979 monograph by Dr. Robyn Cox about earmold acoustics.  In that monograph, Robyn clearly delineates the source of every resonant peak in a hearing aid frequency response, and notes whether it came from a quarter wavelength resonator or a volume/mechanical Helmholtz-like resonator.  I found that the clear explanation allowed me to predict and explain each resonance in the frequency response. As hearing aid bandwidth increased over the following decades, I learned to explain any other resonance in the response.

2. I have always found that the jargon of sound pressure level (SPL) vs. sound intensity was confusing.

Like any field, acoustics is not without its sometimes-confusing terminology.  One word that I have washed from my vocabulary is “intensity”. At almost every turn, I found that I was using that word incorrectly, and this is probably the case for most of the environments that audiologists find themselves in. Intensity is a vector quantity which means that not only is there a value (in dB) but a direction of the noise.  The only area where that is useful is in noise control and where one searches for the noise source. I have only seen a sound intensity meter once in my life at a large convention and it was very expensive.  In contrast, we deal with sound pressure level, or simply sound level every day. This is the proper term to use when dealing with hearing aids, audiometry, and the assessment of the level of noise and music sources. Unlike intensity, sound pressure level is not a vector quantity.

3. Okay, here is an SPL question.  I recall hearing about the “6 dB for every doubling of distance” principle.  Does that really happen in the real world?

Sound is very much like light - both are more spread out and at a lower level the further they are from the source.  A flashlight becomes quite dim as the distance from the source increases and the same is true of the sound field. In an anechoic chamber (or while sky diving), we can have a “free field” where the sound pressure level (and intensity) decreases by exactly 6 dB for every doubling of distance. But other than working in an anechoic chamber (or those of us brave enough to sky dive), we typically find ourselves in a reflective environment caused by walls, floor, ceiling, structures and people in the room. Because of these reflections, in a typical classroom, sound may fall off at 4-5 dB for every doubling of distance as the room acts to reflect some sound. Of course, too much reflection is bad, as is too little.

4. I suspect that with reflection, strange things can happen in acoustics.

That is true.  Reflections, whether they are in a room, a small chamber, or in a tube, can create standing waves that are associated with resonances.  The reflections from one wall or obstruction interact with the incident wave front coming in the other direction to add up constructively (resonance). They also add up destructively where there can be a null.  Actually, there has been some work recently in the realm of “acoustic levitation” where small droplets and particles can be suspended in the null of a standing wave for scientific and medical investigation.  In our field though, the constructive interference, which results in local increases in sound pressure level, are the most important things to know about.  In conventional behind-the-ear (BTE) hearing aids, the sound from the receiver interacts with the sound reflecting back from the end of the earmold bore to create a resonance at about 1000 Hz. This is also known as a tubing resonance.  This is related to the 75-mm pathway between the two acoustic ends.  For children and infants, this pathway is shorter so the tubing resonance appears at a slightly higher frequency.

5. Are there wavelength resonances in custom in-ear products as well?

There are no wavelength-associated resonances in in-the-ear, in-the-canal, and completely-in-the-canal hearing aids.  Given the short pathway between the hearing aid receiver and the end of the shell (perhaps 10 mm), the first wavelength resonance would occur at 8500 Hz, which is beyond the bandwidth of most modern hearing aids.  Any resonances that are observed are related to the mechanical characteristics of the hearing aid receiver.  Today, many mini-BTE hearing aids are fitted with thin tubing and there would be tubing-related resonances at about the same frequencies as would be observed with conventional BTE hearing aids.  The peaks with thin tube BTE hearing aids would be slightly less peaky than those generated with conventional BTE hearing aids. 

6. What about resonances in music?  Is this the same thing?

Yes, but in music (and in speech acoustics) there are three different types of resonances: quarter wavelength resonances, such as the one we have in BTE hearing aids (and in trumpets and clarinets); half wavelength resonances, such as in the stringed instruments and piano; and, Helmholtz or volume-associated resonances, which we see with percussion musical instruments.  The two wavelength-associated resonances depend on the “boundary” conditions or how the vibrating source is held at its end.  In the BTE hearing aid and the trumpet, the vibrating source (receiver diaphragm or the vibrating lips of the musician) is considered to be closed, and open at the other end where sound comes out.  This results in a quarter wavelength resonance.  In a violin and guitar, both ends of the string are held rigidly; this results in a half wavelength resonance.  And, a Helmholtz resonance can be found whenever there is semi-trapped air and a rather small hole where the air can escape. You can see this while blowing across the top of a soda bottle or when you hit a tympani drum.  In speech acoustics, all vowels other than the reduced central vowel /a/ as in ‘father’ are Helmholtz-related vowels. They are defined by the degree of constriction between the tongue and the top of the mouth, and the volume of air behind the constriction.

7. Getting back to hearing aids, when standard earmolds were popular, we had stepped-bore designs, in particular several styles developed by Mead Killion.  This was later mass-produced by Cy Libby and became known as the Libby Horn. 

Libby horns are still selling, albeit not to the extent that they were in the analog era of hearing aids.  These formed pieces of earmold tubing extend from an inner diameter of 1.96 mm to a flare of either 3 mm or 4 mm.  All flares are based on the acoustic transformer effect principle whereby the sound level of all sounds are enhanced in the higher frequency region.  The enhancement does depend on the total length of the tubing and flare, but for BTE hearing aids, the enhancement was for frequencies above about 2200 Hz. As you know, this is a region that is inherently difficult to amplify with hearing aids.  The larger cross-sectional area of the flare provided a lower impedance for the higher frequency sounds; as a result, they could be enhanced by 6 dB (for the 4 mm Libby horn).  One could obtain 6 dB more free high frequency gain and output without any compromise of the battery life!  The advantage of enhancing the higher frequency region by acoustic means rather than just turning up the gain digitally is that: 1.) battery life is not affected; and, 2.) both the gain and the output are increased.  In contrast, with digital methods, given the limitations of many hearing aids in the higher frequency region, it may not be possible to achieve sufficiently high outputs.

8. Do we really care whether something is a quarter or a half wavelength resonance?

In the larger scheme of things, it doesn’t really matter, but in the understanding of hearing aid acoustics (and also speech acoustics) one needs to know the various properties of each resonance.  For example, in quarter wavelength resonators such as in BTE hearing aids, resonances occur rather sparsely - at odd numbered multiples of the fundamental.  Therefore, not only is there a resonant peak at 1000 Hz, but also at 3000 Hz and 5000 Hz (and 7000 Hz) as well.  Acoustic damping of the 1000 Hz resonance can also have an effect on these higher frequency resonances.

9. Does this have any implication for the best musical instrument for a child with hearing impairment to play?

Yes.  In any given bandwidth, a half wavelength resonator musical instrument would have twice as much energy than a quarter wavelength musical instrument.  This may correlate with twice the amount of auditory information.  When playing middle C for a trumpet, there would be energy at roughly 250 Hz (close to middle C), 750 Hz (3 x 250 Hz), 1250 Hz (5 x 250 Hz) and so on.  But if one was playing the cornet which looks like the trumpet but flares in a constant uniform manner and functions as a half wavelength resonator, the energy of middle C would be 250 Hz, 500 Hz (2 x 250 Hz), 750 Hz (3 x 250 Hz), 1000 Hz (4 x 250 Hz).  In short, a cornet would have twice the amount of energy cues than the trumpet because it is a half wavelength resonator.  This would provide child with hearing impairment twice the amount of energy cues. The same argument holds for the clarinet and for the oboe - both look similar, are closed at one end (reed) and open at the bell end, but because of the cone-shaped flare, the oboe functions as a half wavelength resonator.  This “more acoustic cues” argument is mere conjecture, of course, and would make for a wonderful Capstone project for any interested AuD student.

10. Now I am really confused!  Both the trumpet and the cornet are “closed” at the mouth piece end and “open” at the end of the bell.  Why aren’t they both quarter wavelength resonator musical instruments?

I agree that this can be confusing. The primary element in deciding the nature of a resonance is indeed the “boundary” conditions at the two ends.  However, it also relates to whether there is a constant flaring (e.g. cornet, oboe, saxophone, tuba) or an “exponential horn” (such as a trumpet or French horn).  It turns out that if there is a constant flare (you should be able to hold a ruler or straight edge against the side to verify this), then seemingly quarter wavelength resonators function more as half wavelength resonators.  The math is not difficult (and only uses high school trigonometry) but let’s save that for a later date.  The interesting thing is that some ear canals have a constant flare, and despite the fact that healthy ear canals are closed at the eardrum side and open at the meatal opening, they may indeed possess some features of both quarter and half wavelength resonators.  I have written about this and question whether the so called “concha resonance” is truly related to the concha, or if it is merely related to a half wavelength resonance of this inch long (25 mm) tube.

11. Speaking of ear canals, impacted cerumen sometimes results in a high frequency conductive loss.  Can you explain that?

The human ear canal (at least to a first approximation) is a tube that is closed at the eardrum end and open at the meatal opening end so it functions as a quarter wavelength resonator.  Because of the standing wave that creates this resonance, there is very little particle (also known as “volume velocity”) movement near the ear drum (the closed end) but a maximum movement near the open outside end. Like placing you finger near the very end of the guitar strings, there is very little dampening of the sound but there would be a high degree of dampening if placed near the middle of the string. Cerumen, if it is rather lateral (nearer to the open end), will destroy this natural high frequency ear canal resonance, resulting in a high frequency conductive hearing loss.  If the cerumen has been pushed further down the canal, there may be a flatter associated conductive hearing loss.

12. Let’s stick with the ear canal for a little longer.  I hear a lot of talk about using the real ear to couple difference (RECD) when fitting children.  Is this related to Boyle's Law, or is there more to it than that?

In the 1600s, Professor Robert Boyle discovered that in any enclosed space like a balloon or an ear canal with an occluding earmold, the pressure is inversely related to the residual volume.  If we sit on a balloon, the volume is decreased so the air pressure increases until the balloon explodes.  In an ear canal, a long bore will have a resulting lower volume with a higher generated SPL.

13. Earlier you mentioned the word impedance and I know that many of my colleagues start to cringe when they hear that word, especially when we are talking about RECDs.

That is true. Audiologists tend to like to talk about equivalent volume rather than impedance. I must admit that I also begin to sweat when I hear the word impedance but I have a trick that I use if I get confused about the usage of that word. I envision a brick wall built across the frequency scale. For the lower frequency sounds, the brick wall is translucent and I can almost see through it; for the higher frequency sounds, the brick wall in indeed a solid brick wall. High frequencies “see” only what they see in the higher frequency region.  If we are talking about hearing aids, the amount of gain generated in the ear canal is a direct result of the volume of air trapped between the end of the earmold bore and the ear drum. It does not see any further in. As I mentioned earlier, Boyle's Law (volume is inversely related to pressure) defines the generated sound pressure level. So, for higher frequency sounds there is a “lower equivalent volume”.  For lower frequency sounds, the volume between the earmold bore and the ear drum is seen and also the middle ear structures downwind as well. The equivalent volume is therefore much larger with lower sound pressure levels being generated. This has ramifications for the RECD measures especially for those people who have flaccid middle ear systems perhaps due to recurrent middle ear infections. The resulting RECD in situations like this will provide erroneous results in the lower frequency region.

14. Are there any formulae you can remind me about that will make me look smart at parties with friends? 

Certainly!  The quarter wavelength resonator formula is F = (2k-1) v/4L where v is the speed of sound (I usually use 340,000 mm/sec), and L is the length of the tube (in mm).  And the (2k-1) multiplier is a fancy way of saying that the v/4L part is multiplied by 1, 3, 5, 7 and all odd numbered multiples.  The half wavelength resonator formula is merely the simpler F =kv/2L where again, v is the speed of sound and L is the length.  The v/2L part is then multiplied by integers of k (1, 2, 3, 4…).

15. Can you simplify this for me even more?

I see what you are getting at. In all acoustic formulae, the speed of sound is on the top of the equation and the length is on the bottom.  While it’s true that we can’t change the speed of sound, knowing that the length is always on the bottom means that longer tubes have lower resonant frequencies regardless of their physics.

16. Can you give an example to illustrate that principle?

For anyone who has seen commercials about (or can afford to own) a Dyson vacuum cleaner, a quarter wavelength resonator is used as a muffler inside the vacuum tube. When they were first built, Dyson vacuum cleaners had an unfortunate 1000 Hz whine. Dyson immediately constructed a small tube that ran off the main vacuum pathway.  The small tube was open at the vacuum tube end, closed at the other end, and had a resonance of 1000 Hz. This sound would enter the side branch tube and thereby be removed from the sound of the vacuum. The whine was gone and the vacuums were much quieter as a result. Car manufacturers have been using this principle to build quieter cars for almost a century. Automotive muffler systems also use a “side branch” acoustic resonator.  We also see this in speech acoustics in the study of nasals where the oral cavity in the mouth acts as a side branch resonator and removes sound energy from the nasal air flow.  We call this an “anti-formant” and these locally low energy regions help us distinguish amongst the various nasal sounds.

17. Well, vacuum cleaners are not listening devices. Can you give me an example of where that is used in the field of audiology?

Certainly! I know of one example where a manufacturer designed a dynamic earphone for listening to music. It sounded quite nice except for a resonance that occurred at about 4000 Hz.  The manufacturer created a side branch resonator that “sucked” the 4000 Hz resonance out of the sound pathway (and it was trapped in the side branch).  The earphone needed to be slightly thicker in order to accommodate the side branch resonator, but the frequency response was now ideal.

18. One thing that we have not talked about yet are the directional characteristics of loudspeakers?

When you purchase audio equipment, every loudspeaker comes with its own directional sound pattern specification sheet.  In all cases, the loudspeaker becomes more directional or laser-like for the higher frequency region. In contrast the woofer and bass speakers generate sounds that actually go in all directions - they are not directional.  That is why you can place a subwoofer anywhere in a room (including behind the couch) and the effects will be the same.  Higher frequency speakers (tweeters) need to be aimed right at the listener for the full range of that band to be heard.  For years, we have been told by the in-ear monitor manufacturing field that impressions for in-ear monitors need to be as long as possible so that the receiver(s) can be aimed right at the eardrum.  While this is true for loudspeakers in rooms, this does not follow for the acoustics of small enclosed spaces such as the ear canal.  There are many over-the-ear monitors that provide high quality of sound on par (or in some cases, even better) than those that are designed to fit in the ear.

19. Musicians’ earplugs seems to use acoustics to do their magic - how is this done?

Normal earplugs (such as foam plugs) that occlude the ear generally only provide slight low frequency sound attenuation (up to 25 dB if deeply seated) but up to 40 dB of mid-frequency and high frequency attenuation. This naturally-occurring characteristic of hearing protection is less than optimal. Occupational workers tend to remove their hearing protection in order to communicate with their friends and colleagues thereby reducing its effect. And for musicians, one does not want to alter the important balance between the low frequency fundamental energy and the higher frequency harmonic structure. Musicians’ earplugs, first commercially available in 1988, use either a Helmholtz resonance or a quarter wavelength resonance to re-establish the higher frequency sound that is typically lost with occluding earplugs. The result is a flat or uniform response. These acoustic “passive” approaches to hearing protection have certain benefits such as not using batteries.

20. So most of the world’s problems can be solved with good acoustics?

You are absolutely correct.  The acoustics that Thomas Edison used in the horn on his early 20^th century Victrolas, the acoustics of the vocal tract, the acoustics of hearing aids, and those of other commercial devices such as quieter vacuum cleaners and automobile mufflers are all identical.  A well-trained audiologist should be able to apply his or her knowledge of acoustics equally as well in the auto industry as in the audiology clinic.  But alas, acousticians can’t yet solve the mysteries of the common cold.

References

 Cox, R.M. (1979). Acoustic aspects of hearing aid-ear canal coupling systems. Maico Monographs in Contemporary Audiology, 1, 1-44.