THE PRINCIPLES OF TRACKING submarines and other objects underwater have, perhaps surprisingly, remained largely intact since early this century. One simple means is to lower a hydrophone into the water to pick up sound. Indeed, this column described how to build such a device years ago [see "The Amateur Scientist," March 1964 and August 1970]. A more active approach sends sound waves that echo Off a target. Objects of various shapes, sizes and composition reflect sound waves differently. This acoustic signature enables a listener to determine whether an enemy submarine or some other object is approaching [see "Third World Submarines," by Daniel J. Revelle and Lora Lumpe, page 26]. Although the military relies on sophisticated electronic equipment to decipher the echoes, a simple, low-cost transducer can illustrate the essential principles. Easy to build, such transducers are also much cheaper than commercial fish finders, which operate in a similar way.

The basis for the transducer design is a piece of piezoelectric ceramic. When squeezed, this substance develops an electrical voltage across its ends. Conversely, applying a charge to the faces makes the material flex. An alternating voltage causes the ceramic to expand and contract in succession, yielding an acoustic wave. Acoustic waves likewise cause an alternating charge to develop across the faces of the ceramic. Measuring the characteristics of the voltage indicates the kind of object from which the sound waves are reflecting.

The ceramic used for this construction is Navy type-I lead zirconate titanate or Vernitron type PZT-4. It can be obtained in several forms from various manufacturers. I got mine from EDO Acoustics (Ceramics Group, 2645 South 300 West, Salt Lake City, UT 841 15; telephone: 801-486-2115). You will need a ring of the material that is half an inch thick. A ring breaks up unwanted vibration patterns that exist radially through the disk and that compromise its performance. The disk should have a two-inch outside diameter and a 3/g-inch inside diameter. It is probably best to order the piece as a ring, as drilling holes through ceramic is not a trivial process. I had to send mine out, and it cost me $25. Make sure you purchase a ceramic that is polarized through its thickness and has both faces silvered. Building the transducer means connecting a couple of wire leads to the ceramic disk and then mounting it in a suitable housing. Cast-iron pipe fittings, available from hardware or plumbing supply stores for about $5, make a good container. I used a pipe two and a half inches long and half an inch in diameter and a pipe converter. The converter is just a piece of tubing wider on one end than it is on the other. The tail end of the pipe converter should be half an inch wide so that the other pipe can screw into it. The mouth should be just wide enough to accept the ceramic. I used one whose mouth end was two inches wide, but I had to machine the threads out to give myself room to work. File smooth the top surface of the pipe converter and connect the pipe to the tail of the converter [below right].

Next, prepare the ceramic for mounting. Begin by soldering a short lead to each face of the disk. To further suppress unwanted vibrations in the ceramic, you will need some Corkprene, a pliable, corklike material (made by Armstrong World Industries in Lancaster, Pa.; grade number DC-100). I received a three-foot-square, 1/16-inchthick sheet courtesy of Expanco Cork Company (P.O. Box 384, 1139 Phoenixville Pike, West Chester, PA 19380; telephone: 610-436-8300). Wrap the perimeter of the ceramic with the Corkprene and attach two additional layers to the back face of the disk. To connect the Corkprene to the ceramic, use Pliobond, an adhesive available at hardware stores. With the leads and cork in place, the ceramic is ready for mounting.

Prepare the housing by threading some coaxial cable up through the narrow end of the pipe assembly. The cable should extend at least 20 feet. Pull it through so that about an inch sticks out of the top of the housing. Secure the cable in place by wrapping the narrow end of the housing with heavy tape. A tight seal is important.

The next step is to fill the bottom half of the housing with a polyurethane potting compound. I used Conap EN-4 polyurethane (Conap, 1405 Buffalo Street, Olean, NY 14760; telephone: 716-3729650). Follow the package instructions in preparing the compound. Pour enough to fill the mouth end of the pipe converter halfway, but be sure to leave enough room for the ceramic and Corkprene. After the polyurethane sets (about 24 hours), trim the coaxial cable as closely as possible to the polyurethane. Cut the cable so that the center conductor and shield are visible (be sure they do not touch each other).

Insert three or four pieces of short, stiff wire into the dried polyurethane. Cut pieces from sewing needles will work. These pieces hold up the ceramic disk and allow polyurethane to flow under it. Place them so that the ceramic will sit level to the front of the housing, about 1/8 inch below the lip. Solder one of the leads to the center conductor of the coaxial cable and the other to the cable's metal shield. Place the ceramic on the stiff wire pieces and pour in polyurethane all the way up to the brim of the pipe converter. (The polyurethane will not affect the function of the ceramic.) For best results, pour slowly and try to prevent any air bubbles from forming, especially on the front face of the transducer. Allow it to set for 48 hours.

To make full use of the transducer, it is necessary to calibrate it. First, determine the frequency at which the transducer vibrates most readily. This value, called the resonance frequency, can easily be calculated from the dimensions of the ceramic. For a thin disk in the arrangement described, the resonance frequency in kilohertz is equal to 80 divided by the thickness of the ceramic in inches. For a half-inch piece of ceramic, resonance should occur at 160 kilohertz. A more accurate determination demands the self-reciprocity calibration technique. This method, presented formally in Principles of Underwater Sound, by Robert J. Urick, requires three pieces of electronic equipment. The first instrument is a signal generator, which must be capable of running in a pulsed mode at frequencies between 100 and 200 kilohertz; I used a Hewlett-Packard 3314A function generator. The second piece of equipment is a signal amplifier, which must be able to handle high frequencies without distortion. Finally, you will need a two-channel analogue oscilloscope. Although certainly not household items, such devices can usually be found in the physics or engineering laboratories of most colleges and universities. You might be able to arrange to use the equipment at a local institution. A calm water surface is also crucial. An indoor swimming pool, or even an outdoor pool on a calm day, suffices nicely. A bathtub or a 55-gallon drum is probably too small to yield accurate results. The transducer must be held in a mount that can be rotated. At the laboratory, we use a sophisticated computer-controlled system, but an expendable camera tripod and a clamp should do the job.

Calibrating the transducer requires measuring the voltages across the faces of the device and the current transmitted through it. Run the input signal from the signal generator to the amplifier. Connect the transducer to the amplifier in series with a 600-ohm resistor preceding it and a 10-ohm resistor directly after it [see Figure 1]. The voltages transmitted and received can then be measured directly across the transducer and displayed simultaneously on the oscilloscope. The voltage drop across the 10-ohm resistor gives the transmit "current." To determine the actual current, display the signal on the other channel of the oscilloscope and divide the measured voltage by 10 ohms.

After setting up the circuit, place the transducer in the water so that it points up at about eight to 12 inches below the surface. Set the signal generator and amplifier to provide pulsed sine waves. The transmit voltage should be around 20 volts peak to peak (that is, 10 volts above and below zero). On the signal generator, set the frequency at 160 kilohertz (or whatever number you determined to be the working frequency of your transducer) and the number of pulses at 35. The oscilloscope should show a distinct transmit signal of 10 volts strong and 35 cycles long, followed by a weaker "echo" of the same duration as the transmit signal. This echo is the first reflection from the sound scattered by the water-air interface. In fact, there should be a train of echoes corresponding to second and third and even fourth reflections. These reflections are strongest when the transducer points straight up. To take measurements, apply as much gain as you can to the device without distorting the transmit voltage on the oscilloscope. Then record the levels of the transmitted voltage, the received voltage (the level of the first reflected pulse) and the transmitted current.

These measurements will enable you to determine the transmit signal and receive sensitivities of the transducer. These characteristics depend on the transducer's impedance. The method for calculating the impedance appears in the box on the left. You must carry out the procedure for a range of frequencies centered on the theoretical working frequency. The results will allow you to pinpoint the exact frequencies at which your transducer is most sensitive.

To determine your transducer's directivity, or beam pattern, set the frequency back to where it is most sensitive. Mine was 156 kilohertz. After making sure the transducer is pointing straight up, take a measurement. Rotate the transducer in one direction by one or two degrees before conducting another measurement. Continue this procedure until the first echo no longer appears on the oscilloscope. Reset the transducer so it is aimed straight up again and repeat the entire procedure, but rotate the transducer in the other direction.

Once you have your data, you must "normalize" your results. That is, divide all your measurements by the result

obtained at zero degrees, or looking straight up. Take the logarithm of these normalized quantities and multiply by 20; this procedure converts the readings into decibels. Plot these values on the y axis against the angles for which the readings were taken on the x axis. (Note that the decibel values are negative, so that zero should be at the top.) You should get some kind of bell-shaped curve, with the maximum occurring at the zero-degree mark. Look for the points on the curve that are six decibels below zero. The expanse of the curve at this point indicates the effective beam width

After you determine the operating characteristics of your transducer, you can use it for many purposes. You can determine the position of a large object by looking for its echoes. Multiply the time between transmit and receive pulses by the speed of sound in water (about 1,500 meters per second) to calculate its distance. If the target is moving, you will need to repeat the procedure several times to track its distance from the transducer.

Because most amateurs will probably not need to locate submarines and torpedoes, it is perhaps more practical to observe how different surfaces scatter sound waves. To start, I would suggest scattering signals off the bottom of a swimming pool. Many aboveground pools have a sandy bottom covered by a pool liner, which is acoustically transparent. Another good surface would be an in-ground pool, which often has a rough concrete bottom.

Take at least 100 separate measurements at a time, scanning the surface with the transducer positioned at a known distance and angle from the bottom. You must then manipulate the data statistically [see box above]. Each kind of surface will produce a characteristic curve. Urick's book offers several examples. With this information and your transducer, you should be able to deduce the kind of bottom below bodies of water down to at least 30 meters deep.

For more information on scattering curves, write to: The Amateur Scientist, Underwater Transducer, Scientific American, 415 Madison Avenue, New York, NY 10017-1111.

Bibliography

FUNDAMENTALS OF ACOUSTICS. L. E. Kinsler, A. R. Frey, A. B. Coppens and J. V. Sanders. John Wiley & Sons, 1982.

PRINCIPLES OF UNDERWATER SOUND. R. J. Urick. McGraw-Hill Publishing, 1983.

UNDERWATER ACOUSTIC SYSTEM ANALYSIS. W. S. Burdic. Prentice Hall, 1984.

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