Most importantly, why was this so interesting to be posted on a blog concerned with RF. Well, to my very own understanding, the principles behind emitting sound waves it somewhat similar to the principles of emitting radio waves.
Here is why:
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| Analogy between a quarter-wave vertical and a quarter-wave speaker enclosure |
On the right hand side, you see a loudspeaker cabinet called quarter wave pipe (QWP). In such a pipe design, similar to the gamma-match of the vertical, a driver (in acoustics loudspeaker chassis are called drivers) creates pressure waves (green) somewhere in the middle of the "conductor". Similar to a quarter-wave antenna, the conductor is excited at a resonance frequency. The blue line indicates the air speed, i.e. current, through the pipe. The red arrows indicate sound emissions.
- The driver emits sound to the front side of the cabinet.
- The standing wave emits sound at the open end of the pipe.
Consequently, the bandwidth of the pipe needs some severe broadening!
Back to aerials, there are 2 ways to make an antenna broadband:
- add more resonators (e.g. log-per, dipole fan)
- add Ohmic resistance (e.g. T2FD, Beverage antenna)
In acoustics, one can add more resonators by tapering a restrictive volume and add resistance by stuffing said volume with dampening material.
For a HiFi speaker cabinets one needs a very homogenous emission over several octaves, i.e. close to 0Hz up to 22kHz (those are, of course, extremes). A mixture of multiple resonances and some severe resistance is used. Actually, there is an added bonus on the resistive part of things... not only does stuffing material add resistance, it also lowers the velocity of sound within the medium. A stuffed enclosure looks larger to sound-waves than the same enclosure not being stuffed.
PVC piping, at last we leave the theory part of things, is a very convenient stuff to work with. Now we talk about pipe in the sense of water pipe. Have I forgotten to mention that the word pipe could have several interpretations, sewage pipe, water pipe, organ pipe, pipes of bagpipes, etc. OK, pipes, i.e. PVC pipes, fittings and stuff thereof. Here is the B.o.M:
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| PVC parts |
- tubing form the pipe's body, obviously
- the elbow is the resonator's "mouth", bending pressure waves towards the listener
- the T-piece is to the driver
- the reduction pieces will taper the resonator
- and the end cap will be the end cap, i.e. terminating the resonator.
The upper part of the pipe is tapered down to 2" and 1.5" PVC tubing. The respective tubes have a length of 50cm each. Obviously, fittings add length to the final product.
Adding 1 additional diameter to the taper, will just add 1 more resonance (and its harmonics). Hmmm, "Two Not Bass Samba", really?! No, that does not help!
The tubes therefore receive insets. The process of making those is pretty easy. My preferred method is using heating pipe insulation foam tubing. Cut in half, the stuff can be easily be cut diagonally. A result of this is tapering for pressure waves.
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| Tapering inserts |
However, before putting everything together, we need to address the resistive part of broadening the bandwidth of the pipe and lowering its resonance. There is no photo of this step. The material involved is polyester from an IKEA pillow, the cheapest acoustic stuffing on the market!
I complemented the inserts with the pillow stuffing and shoved it down the respective 50cm PVC tube.
We are nearly finished... there is just one other addition, before the "cabinet" can be assembled. In order to prevent the creations of unwanted harmonics, dampening material (cleaning cloth!) has to be added behind the driver (within the T-piece).
Here is a photo of the finished speaker:
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| The Alphorn speaker |
The sound of those speakers is amazing! From classical to hiphop, via kizomba, funk and rock... the sound of those speakers blows me away!
Mind you, those are very cheap 3" drivers...
The drivers came in a stereo set priced less than €40.
Why am I mentioning this? The price for the PVC plumbing parts, used for this project, is actually > €42.The passive parts of the project exceed the price of the active ones... not sure what that means in the context of modern electronics.
Speaking money, the Alphorn speakers sound like speakers in excess of at least 1k€.
Back to theory... the total length of the pipe is about 225cm. 2,25m in quarter-wave reflects 9m of wavelength, which in itself equates to a sound frequency of about 33Hz. This would be the resonance of the empty (non-tapered) pipe.
As said before, the upper part of the pipe is stuffed with IKEA pillow material, hence the real resonance frequency will be even lower. Stuffing enclosures is called "Mass Loading".
There are 2 sharp steps in the taper, one at 120cm and one at 175cm. Those steps add resonances at 62.5Hz and 43Hz, which of course will also have harmonics too.
The resulting speaker enclosures qualify for the MLTQWP... and... they sound amazing!
UPDATE on alternative design thoughts. Thoughts only. On the internet a couple of designs float showing curved structures, involving a plurality of bends and elbows. Similarly to stepped tapers, those bents create reflections and disturb the air-column of the standing wave pretty good. Bending the design to limit height of the speakers seems however a very attractive thing to do.
My gut feeling tells me that 45º bents at carefully selected lengths could work. Maybe two of those just above the feeding T, followed by a reducer and two more 45º bents. Such a design would keep the tallness of the speaker at about 140cm. However, I still believe that such a measure will reduce the amplitudes of the lowest frequencies.
