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 resonant peak.
    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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