Acoustically Resonant Loudspeaker
A loudspeaker connected to a communications receiver
should have limited frequency response. For voice reproduction, frequencies
between 300 - 2700 Hz. contain useful information. For Morse code reproduction,
a much smaller bandwidth, centered about 700 Hz. would be useful. This
note describes how a small dynamic loudspeaker can be adapted to give a
resonant peak at 700 Hz.
A bare loudspeaker has an inherent resonance. Its cone mass resonates
with suspension compliance at a low audio frequency. At this frequency,
cone motion is maximum. We'd like the cone to move as much as possible
to create high-amplitude sound waves.
You may not be able to hear a "peak" at the speaker's
inherent resonant frequency, because the air that the cone pushes out zips
around the speakers edge to replace the air at the back of the cone. The
result is that not much audio power is directed outward to your ears. In
any case, the speaker's inherent resonant frequency is most often a good
deal lower than we want. A small 2-inch bare loudspeaker might resonate
at about 400 Hz. We need to find a way to increase resonant frequency up
to the desired 700 Hz.
A loudspeaker is a dismally inefficient transducer.
That is, the A.C. electrical power coming in is a great deal larger than
the acoustical power delivered as sound waves. Typical efficiency is about
one percent. The primary reason for such poor efficiency is that the air
load on the cone is very light, compared with the driving force. This problem
is very similar to an impedance mis-match, where a low source impedance
cannot deliver maximum power to a high-impedance load. An acoustical transformer
can boost efficiency by a great margin. Just as transmission lines can
transform impedances from low to high, appropriately shaped acoustic cavities
could be employed to address the mis-match. If they do so at only one frequency,
so much the better.
Increasing resonance to 700 Hz.
At 700 Hz, our little 2-inch driver's cone is not
moving much at all. The cone mass dominates, limiting cone motion. If we
can balance the dominating mass with a stiffer compliance at 700 Hz, we
can maximize cone motion, and get more sound. Since cone mass and compliance
only balance at one frequency, we have a resonant condition. At lower frequencies,
compliance dominates, at higher frequencies, cone mass dominates. So maximum
sound only occurs at one frequency.
How can we increase compliance? We can use the compliance of air in a closed
cavity behind the speaker. The smaller the cavity, the stiffer compliance
it will have. The closed cavity will also prevent air from rushing around
the speaker's edge to the back of the cone. An analogous transmission-line
would have a short at one end, and be shorter than 1/4 wavelength long.
What is the right size cavity? The speaker that
you choose to use may have a different cone mass (and resonant frequency)
than another, so there is really no fixed cavity size appropriate for all
speakers. Note that cavity depth is relatively unimportant here. There
are other (longer) lengths of tubing that could provide the same compliance,
but I've selected the shortest, smallest cavity possible. A small cavity
is easier to make stiff. At 700 Hz., even stiff materials flex somewhat,
which adds losses.
Another possibility is to use an open-ended tube.
This solution requires a much longer tube, but can provide a more selective
I built a complance-tuned speaker using a small
2-inch driver from a transistor radio (shown above). The speaker's outside
edge sat in the rim of a 2 + 1/8" aluminum tube. The tube length was adjusted
to give about 700 Hz. resonance: it ended up one inch deep. Once
again, a bigger cavity will lower resonance - a smaller cavity will resonate
at a higher frequency. A thick sheet of aluminum was cut to close off the
end of the tube. Hot-melt glue holds everything together. Selectivity of
this resonator is quite narrow (possibly too narrow) at about 150 Hz. Such
narrow bandwidth can cause ear fatigue.
There is another advantage of this speaker. Even
though I used an eight-ohm speaker, its impedance at the resonant peak
is about 23 ohms! This means that less AC current flows, and less power
is required of the audio amplifier. More volume with less power - a QRP
device if there ever was one.
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