Directivity and high frequencies

Marshall Chasin
August 28, 2012

Almost daily I am asked to make “deep-seated” earmolds for hearing protection and monitoring devices in the performing arts.  Clients come in and state that this must be done, even before I get to ask them their names.

I must admit to being partly to blame since I helped to write the minimum requirements for many manufacturers of earmold technology.  All I really did was to summarize what we learned in school and combine it with the current literature that appears in our field.  However, in many cases, people’s ear canals are just too narrow, or have many bends, which means that making a deeply seated earmold impression for an ear monitor or a hearing protector very difficult.   And even if we could make a device with a long ear canal bore, it may be almost impossible to insert it into the ear canal.

There is nothing special about it, but here is why I recommended it (for those who have been blessed with elephant-sized ear canals).

Managing the characteristics of sound is like herding cats.  If you have ever tried to get four or five cats to go into a room, they seem to go in five or six directions.  Unless you have a really good cat treat, cats do what they want to do.  I guess that that makes them cats.  This is especially true of lower frequency sound.  I can have a loudspeaker (or a person’s vocal tract) and for lower frequencies, sound emanates from the side as much as from the front.   The next time that you are near the bell of a trombone or a tuba, use a sound level meter (or one of the great sound level meter apps on your favorite smart phone) to measure the sound level at 2 feet directly in front of the bell, then 2 feet to the side of the bell, and even 2 feet behind the bell. No difference.  Well, a very slight difference.

Low-frequency sounds do not see the wall of the musical instrument, or the tubing from the receiver in an in-ear monitor as an obstruction.  These sounds don’t bounce around- they simply don’t see the wall as a “wave guide.”  This has a lot to do with the length of the low-frequency wavelengths.  As the name suggests, low-frequency sounds are infrequent and it takes a larger distance to complete a full wavelength.  And, as  a rule of thumb, an obstruction needs to be a significant portion of a wavelength before that obstruction can alter the direction (or level) of the sound.   If you have noisy neighbors and poor windows in your house, there will be minimal attenuation of the low-frequency components of the party going on next door. So, if you have lousy windows, make friends with your neighbors so at least you will be invited to their parties.

Low-frequency sounds are omnidirectional, and, like cats, they do what they want to do.  I can “aim” the receiver of a hearing aid or an in-ear monitor almost into the ear canal wall, and for lower frequency sounds there will be no difference.

Well, the title of this blog is “Directivity and high frequencies,” so let’s talk about the higher frequencies.  Higher frequencies are obedient nerds that do exactly what you want them to do.  These make for great students in high school, but tend to get beaten up on occasion.  Nevertheless, you tell a high-frequency sound to do something and it does it without any questions- their homework is always done on time and correctly.  These  do not act like stupid cats.

Higher frequency sounds are “more frequent.”  Their wavelength is shorter and obstructions that would otherwise be acoustically invisible for longer wavelength sounds, now would become significant factors.

The pinna effect is a great example of this.  That small bit of cartilage sitting at the side of the head is too small to be noticed by long wavelength, low-frequency sounds.  These sounds go right past the pinna as if it were not there.  In contrast, the shorter wavelength higher frequency sounds “see” the pinna as an obstruction and reflect back to the ear.  Not only do higher frequency sounds enter the ear directly, but there is significant early reflections to the ear off of the flange of the pinna.  The net effect is a boost of the sound energy that reaches the ear, in the higher frequency region.  Cupping your hand behind the pinna further enhances this effect.  High frequencies can be easily reflected- the pinna can be thought of as an acoustic mirror.

Another, and related feature of high-frequency sounds is that they are highly directional.  If I aim a 6000-Hz sound directly in front of me and measure its sound level in line with the source, I will get one value. But if I measure that same sound off to the side, the sound level will be much less.   High-frequency sound energy is like a laser beam- it goes where you want it, or at least it goes where it’s aimed.

In-ear monitors or hearing aids have a receiver that emanates sound into the ear canal.  The lower frequency components of the speech or music will always make it to the eardrum.  But the higher frequency elements will only hit the eardrum if the speech or music  is aimed at the eardrum.  Well, perhaps I overstated this a little bit. Since higher frequency sounds tend to reflect off of walls, there will be some reflection that makes it to the eardrum even if the sound bore is not aimed in an optimal manner.

Aiming a sound bore in an optimal manner generally means that the bore should be long enough that its outlet is in line with the eardrum.  And this frequently necessitates a long bore for the in-ear monitor, hearing aid, or even hearing protector.

The same can be said of a loudspeaker and its directivity.  If you check on the Internet or in any textbook about loudspeaker design, you will see a chart showing that for lower frequency sounds, the loudspeaker can be oriented anywhere and in any direction, but for higher frequency sounds it functions as a laser beam- it must be aimed at the listener for optimal sound transduction.

Marketers of home theater sound systems talk about 5.1 technology.  This refers to 6 speakers- 5 of them transducing the treble sounds, and one of them being the subwoofer or large bass speaker.  The reason why marketers don’t call this 6.0 technology is that there are really only 5 speakers that we can use to generate the sound that can be sourced as coming from a certain direction (or loudspeaker).  The 6th loudspeaker – the subwoofer- can be placed facing the wall, or even placed behind the couch (as mine is).  Because of the bass characteristic of this 6th loudspeaker, it does not see the couch as an obstruction, and is anything but directional.  Admitting that a 6-speaker system is really only a 5 + 1 speaker system is actually quite honest of the marketers, and obviously speaker designers know a few things about  “directivity and high frequencies.”

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