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Transmission-Line Speaker Design Basics
I've included some links here to very good transmission-line sites that go into considerable
detail, but I thought I'd sum it up for those who want a simple explanation.
A transmission-line speaker design uses the wave off the back of the woofer, delaying it in time
so that it arrives at the front of the speaker in phase with the next wave coming off the front
of the woofer.
The delay is accomplished by means of a long pathway from the back of the woofer to the open air
known as a transmission line. The secret to a good transmission-line is in matching it to the
specific woofer. This is done by obtaining the measurement of the woofer's resonant frequency.
The resonant frequency is the tone that the woofer naturally "rings", much as a bell does.
In the speaker world, this measurement is supplied by the manufacturer as the Fs parameter. In
this case, the Vifa woofer has an Fs of 37hz.
It is then a simple matter of determining the correct length for the transmission line. This is
done by using the following formula:
Length = (resonant frequency wavelength)/4
This is known as a quarter-wave design. The wavelength is determined by using the formula familiar
to all first-year physics students,
Velocity = Frequency * Wavelength
Where velocity is the speed of sound (330 meters per second). We have to
solve for Wavelength, so we divide the velocity by the frequency to get 8.9 meters. To get the
correct transmission-line length we further divide the result by 4 yielding 2.2 meters.
Converting to inches, we get about 85 inches. Now, I'm fudging it a bit here, since our
cabinet height (internally) is only 42 inches so a folded pathway is actually a bit less than
the optimum, but, frankly, the results from listening tests are very satisfying.
It would be interesting to increase the height of the cabinet a bit. I'll give that
a try next time.