The other day I talked about different loudspeaker designs and with the swarm intelligence of all those who helped contribute to the post through the different forums in what sometimes were heated debates. Itnow seems that justice is done to all the different ways to skin the cat.
Now it is time to talk about a particular design of loudspeaker, which of course is near and dear to me: The quarter wave loudspeaker. I am certainly not saying that this is the only way to build loudspeakers, perhaps not even the best. But it is a fantastic way to get amazing sound with a reasonable foot print at unbeatable prices.
When researching for my company a while back, and now for this this blog, I realized that basic information understandable to the layman is hard to come by and usually articles on quarter wave loudspeakers quickly get lost in mathematical formulae and mathematical modeling.
The first big divide is the use of the term Transmission Line vs. Quarter Wave loudspeaker. A transmission line is any loudspeaker that sends the backward sound down a more or less long tube. A quarter wave loudspeaker is a loudspeaker where this tube has a particular length that of a quarter wavelength of a low frequency the loudspeaker is expected to handle without roll of.
I consider it a true statement that all quarter wave loudspeakers are also transmission lines and most good transmission lines are also quarter waves.
It has been known for a very long time that sound can travel a fairly large distance down a tube with relatively little loss and distortion. Shipbuilders have relied on this for communication from the bridge to the engine room for example.
Transmission lines are all around us in organ pipes or wind instruments such as the pipe organ, woodwind and brass and of course in loudspeakers.
As mentioned in a previous blog, with all loudspeaker designs, the big question always is what to do with the sound that radiates backwards from the driver, and there are three basic choices,
live with it,
take care of it,
or use it.
Living with it really isn´t a very good idea, taking care of it makes drivers and speakers rather large, and using it can have surprising benefits if done right.
For a quarter wave loudspeaker we definitely make good use of the sound energy coming from the back of the driver and turning it into something we all like: Bass. We send the sound down a tube that is closed at the top, and restricted but open at the bottom. This tube is wide enough to not provide significant resistance to the airflow and it has a length that corresponds to ¼ of a wavelength of a bass note that we would like to extend to. Now why a quarter? Because we want the sound coming from the open end of the tube to be in sync, or in phase with the sound that comes from the front, so we need to effectively turn it around. A quarter wave lets us do just that.
Now when the loudspeaker driver is expected to play a note that is significantly below its rated capability, a standing wave is formed in the tube with the closed top seeing high pressure and zero motion and the closed end seeing high motion and zero pressure.
This kind of tube then acts as a wave-guide that brings us base notes that are far beyond what we would expect from a driver of any given size. The bass notes are in phase with the output of the driver and there is a very smooth roll off of the bass, meaning that as frequencies get even lower, the notes are still there and congruent with their over tones, as we approach the audible threshold of about 20Hz.
At the same time such pipes can be tuned far below the driver’s resonant frequency without falling into a dominant frequency or the dreaded “one tone bass” that many bass reflex designs suffer from.
This image shows how bass is extended using a quarter wave (actual measurements)
In the graph you will see the response of the driver in green and the output at the end of the tube in red. The trick is to extend the bass beyond wht the driver is capable of, have it´s output in phase with what the driver emits and have a smooth bass roll off, while attenuating overtones. Combine the two by recording the output at a distance, and you will get a rather desireable smooth response over a large frequency range and in phase from a rather small 3 inch driver.
All this requires tremendous tuning and mathematical modeling and quarter waves have become some of the most popular designs in the do-it-yourself community for good reasons. Some of these designs are not exactly practical as they try to accomplish so much bass, that the tubes get rather large, but for those who are willing to trade off with bass notes that are within the real of real instruments, a sleek and small quarter wave like our Sound Sommeliers might be a very enjoyable choice of loudspeakers. They also have fantastic WAF, click on the link, if you don´t know what that is.
Part of this tuning is dealing with the harmonics that form in the pipe. Unfortunatelya quarter wave will not only resonate at the fundamental frequency that corresponds the quarter wave lenghts, but at various overtones. While a well designed quarter wave loudspeaker will have very little overtones, this can be effectively taken care of using acrylic wool in the upper two thirds of the pipe that let the bass notes pass, but resists the faster moving air of the higher frequencies. A nice side effect of this is that the speed of sound in such material is also slightly slower than in free air, making a quarter wavelength for a given frequency shorter. How much shorter? You can look at our lineup of loudspeakers to get an idea of how well and non-invasive a design like that can be integrated into a living environment.