In part 1 of this blog series, the acoustics of the Didgeridoo were discussed showing that like a trumpet or clarinet, the Digeridoo functions as a quarter wavelength resonator with odd numbered harmonics of the equation F = v/4L where v is the speed of sound and L is the length of the tube. The Didgeridoo that I recently purchased is 1.25 meters long (about 4 feet) and resonates at about 68 Hz (with harmonics at 3 x 68, 5 x 68, 7 x 68, and so on). Some Didgeridoos are more conical in shape, like a tuba or saxophone and despite the fact that they are “open” at one end and “closed” at the other end, function more as one half wavelength resonators which in this case has a resonant frequency one octave higher at 2 x 68 Hz or 136 Hz (and with harmonics that are integer multiples of 136 Hz, namely, 136 x 2, 136 x 3, 136 x 4, and so on).
In addition to the wavelength characteristics governed by its length (L), the Didgeridoo has “side branch” resonators that are small channels cut out by termites in its previous tree-incarnation. Since the termites never made it to the outside (and hopefully are not still in there), these side branch channels are also functioning (to a first order) as quarter wavelength resonators.
Even though the diameters of each of these side branch resonators are narrow, there are many of them since the traditional Didgeridoos came from the northern territories of Australia where termites and other crawly bugs are quite common. Their effect may be modelled as the sum of these side branch resonators so the overall effect may be quite significant.
And to add further complication… actually simplification, some of these side branch tunnels carved out by hungry termites can be simple tubes or perhaps volumes where maybe baby termites will emerge when least expected. Acoustically one can say that these side branch resonators are either quarter wavelength resonators (simple tubes as shown below) or Helmholtz resonators (volumes with narrow constrictions such as those heard when one blows across the top of a pop bottle as shown above). It’s really a simplification in the sense that in both cases, energy is removed from the sound that emanates from the Didgeridoo and thereby lost to the listening public.
We can see side branch resonators everywhere, even in our own hearing health care industry. For example, there is a wonderfully sounding earphone from Etymotic Research called the MC-series of earphones. Unlike many other earphones that are based on balanced armature technology, these use a dynamic technology (similar to in-ear monitors from Future Sonics). Many would argue that dynamic earphones are “warmer” and performing artists such as Bono with U2 and Shania Twain, prefer the sound of dynamic earphones. Well, back to the MC-series… when they were first manufactured, there was a small undesirable resonance at 4500 Hz. Etymotic Research engineers, created a small side branch resonator in the earphone that would “suck out” the rogue 4500 Hz resonance, yielding a smooth frequency response. That is why the MC-series of earphones are slightly wider than other products such as Hf5- they have a small side-branch resonator.
Another example of a side branch resonator comes from speech acoustics and how nasal sounds are made. Nasals, such as /m/ and /n/ are found in all languages of the world and have everything to do with our nose. But just as importantly, nasals have much to do with our mouths as well. During the articulation of nasals, the main air flow is through the nose (unless you have a bad cold), but the closed mouth during the articulation of an /m/ or an /n/ acts as a side-branch resonator. The resonance of the oral cavity in the mouth removes some of the nasal energy and an “anti-resonance” or “anti-formant” is created. For those who like to study speech acoustics, the anti-resonance for the /m/ is at 1000 Hz, and that of /n/ is 1700 Hz. This loss of energy at these frequencies helps to characterize an /m/ as an /m/ and an /n/ as an /n/. Unfortunately for those who do not like to study speech acoustics, its still the same thing!
Yet another example of side branch resonators is from Dyson fans and vacuum cleaners. These are the people who create quiet fans and also eerily quiet vacuum cleaners. Dyson engineers noticed that their devices were a bit noisy and upon spectral analysis of the noise spectrum, a large resonance was noted. Well, the engineers (who presumably knew all about Didgeridoos) constructed a side branch resonator that “sucked” the rogue resonance out of the noise spectrum. Dyson has an excellent video of this that I actually use in my speech acoustics class that I teach at the University of Toronto.
And of course, side branch resonators have been around for almost as long as cars- the muffler system on cars uses a side branch resonator to remove some of the unwanted noise emanating from the car engine.
I suspect that since Didgeridoos have been around for at least 1000 years, that the correct sequence of the use of side branch resonators would be: (1) humans and their vocal tracts, (2) Didgeridoos, (3) car mufflers, (4) MC earphones, and (5) Dyson noise control systems.
In part 3 of this blog series, the effects (if any… that’s a hint…) or curves in the Didgeridoo (and that of our own vocal tracts) will be discussed.