R. H. Nichols, Jr. Bell Telephone Laboratories, Inc., Whippany, New Jersey 07981

TECHNICAL NOTES AND

RESEARCH BRIEFS

ACOUSTIC PROPERTIES OF PARABOLIC REFLECTORS

Randolph Scott Little* Laboratory of Ornithology, Cornell University, Ithaca, New York

SxNcr. SOUND POWr• X•XATr•D •O•r A

point source varies inversely with the square of the distance--i.e., drops 6 dB each time that distance is doubledmand since the

apparent area of the radiating surface also decreases to one-fourth its initial value

when distance is doubled, it is often desir- able that a sound-pickup device have both large gain and high directivity. Since May 1932, aluminum or Fiberglas© parabolic reflectors have been used in natural sound

recording to increase the gain and direc- tivity of microphones (Kellogg, 1962), but without accurate knowledge of their acous- tical properties. Recent interest in collapsi- ble or folding sound reflectors points to a need for theoretical and practical study of the characteristics of these reflectors. This

article is based on a report (Little, 1963) to the School of Electrical Engineering, Cornell University, of a project in which theoretical and experimental investigations of this kind were conducted, and is ex- cerpted from a study reported in the Bio-A coustics Bulletin of CornellUniversity.

At high audio frequencies, reflectors of the type generally used in the Laboratory of Ornithology (spun aluminum, 36-in. diam, 12-in. focal length) have high gain and are quite directional. At low frequen- cies, on the other hand, they have little or no gain and are omnidirectional. At intermediate frequencies, gain and direc- tivity are irregular. It is this intermediate range that is of particular interest from the standpoint of analysis.

Examination of the equation for the theoretical gain of a parabolic reflector

(Kinsler and Frey, 1961) suggests that the gain will be low at low frequencies, high at high frequencies, and will experience large variations at intermediate frequencies. These variations will appear as a damped pseudosinusoid as depicted in Fig. 1.

The actual measured response of a 36X12-in. aluminum reflector at 0 ø inci- dence is given in Fig. 2 (a). Notice the large peak at 200 Hz. This is due to cavity

5

I io

Frequency (kHz)

Figure 1.

resonance of the dished reflector, much as in an organ pipe, and is omnidirectional. Effective reflection begins near 1000 Hz, and is quite variable to beyond 10 000 Hz. Although accurate measurement at higher frequencies was beyond the capabilities of the instruments used, it is suggested that these irregularities should decrease at higher frequencies, making the response especially flat in the frequency range of interest in the recording of ultrasonic sounds.

If the parabolic surface of the reflector is approximated by a series of small flat circular facets, each of these facets must be oriented so as to direct reflections through the focal point. In order that reflections from these hypothetical surfaces not differ significantly from those from the true parabolic surfaces, each flat element must not deviate from the true surface by more than about 1% of a wavelength so that phase shift will be less than 10 ø. The

solution of the geometry shows that, if the deviation is to be less than 1%, the radius of a facet cannot exceed O.laL•, where a is the parabolic constant and L is the wave- length of the sound. For a value of a= 10 (typical for the reflectors used), this means that the radius of a facet cannot exceed the

square root of the wavelength. Considering a plane wave incident upon

the reflector, the wavefront may be sub- divided into areas corresponding to the areas of each facet of the hypothetical reflector. Each facet will reflect its cylinder of sound toward the focal point. However, the convergence of all these cylinders of sound will be to a focal region rather than to a discrete point, the cross section of which will correspond to that of the facets. Hence, the size of the focal region is proportional to the square root of the wavelength of the sound, making direc- tivity proportional to the square root of the frequency. The limit of directional resolu- rio n for a 36X12-in. aluminum reflector using a microphone with a 1-in. diaphragm seems to be about 10 ø, occurring at fre- quencies of 5000 Hz and higher. The limit as determined by the L« formula would be about 8 ø at 8500 Hz. The slight loss of resolution by the typical reflector is probably due to inaccurate placement of the microphone at the focal region.

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Frequency (kHz)

Figure 2.

The Journal of the Acoustical Society of America 919

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TECHNICAL NOTES AND RESEARCH BRIEFS

Folding Reflector

Experiments conducted on a collapsible umbrella reflector, recently made available to the Laboratory of Ornithology by Rodman Ward, gave very encouraging results. The device, sold under the trade name of Reflectal©, is a Nylon© fabric umbrella with roughly parabolic shape when set. The reflecting surface is of aluminized Mylar© bonded to the Nylon, with a fine quilted texture to diffuse light rays. The reflector was intended for use in floodlighting photographic subjects, with no provision for mounting a microphone at the focal point. At the time of this writing, suitable fittings are being prepared; but preliminary measurements were conducted with the microphone held in place by a separate tripod. The focal length appears to be about 12 in., the diameter about 40 ins.

The results are quite comparable to those for the conventional aluminum reflectors, as shown in Fig. 2 (b). Over-all gain averages several decibels less for the fabric reflector because of less efficient reflection. Due to

the imperfect parabolic shape, the limit of directional resolution is somewhat poorer

than the 10 ø found for the conventional aluminum reflector.

Conclusion

Once the microphone mount has been prepared, and the Reflectal has been field- tested, a more accurate evaluation of its practicality will be possible. However, based on laboratory tests, the collapsible umbrella reflector promises to give per- formance comparable to that of a rigid reflector of equal size, at about one-quarter the weight and one-twentieth the (folded) volume. This could amount to considerable

advantage from the standpoint of trans- portation, especially where shipping is a factor. The main features yet to be proven are the durability and convenience of use in the field.

These results indicate that a 36-in.

reflector of rigid construction may be thought of as a 20-dB amplifier with a high- pass filter network that cuts off at 1000 Hz. For recordings of bat sounds and other ultrasonic sounds, reflectors of smaller

by the 200-Hz peak, the microphone should lie outside the plane of the rim of the re- flector. On the other hand, in order to suppress sounds coming from directions behind the reflector, the microphone should be well inside the rim. A suitable com-

promise is to place the microphone at the plane of the rim. This means that the focal length must be one-quarter of the diameter in order to satisfy the formula for a para- bolic curve. In the analysis of sound record- ings made with a reflector, the analyst should be aware of the irregularities of frequency response brought to light in this paper, especially the low-frequency cutoff, which might otherwise be attributed to acoustical filtering in the voice-producing system of the animal.•-•

* Present address: Bell Telephone Labs., Inc., Columbus, Ohio. Kellogg, P. P., 1962. "Bird Sound Studies at Cornell," Living Bird 1, 37-48. Kinsler, L. R., and A. R. Frey, 1961. Fundamen- tals of Acoustics (John A. Wiley & Sons, Inc., New York).

diameter can be used without sacrificing Little, R. S., 1963. "An Investigation of the uniformity of frequency response. In order' Acoustic Properties of Parabolic Reflectors. Cornell Univ. School Elec. Eng. Senior Proj. to avoid deep cavity resonance, as indicated Rept. (unpublished).

PROCEEDINGS OF MEETINGS ON ACOUSTICS IN NAVIGATION

Ta-E O•owrNo INTEREST IN EMPLOYMENT

of acoustical methods for navigation of ships and submersibles is highlighted in the recently published Manned Deep Sub- mergence Vehicles Proceedings. This 317- page volume comprises papers presented 20-22 January 1966 at the National Marine Navigation Meeting in San Diego, Cali- fornia. The meeting was sponsored by the Institute of Navigation, with the partici- pation of the Marine Technological Society. We are indebted to the chairmen of two of

the sessions, K. V. MacKenzie (U.S. Navy Electronics Laboratory) and D. J. Klein (Autonetics Division of North American Aviation), for the following notes on some of the papers that involved acoustics.

Session D: K. V. MacKenzie, Chairman

The general subjects included (1) navi- gation of support ships to pinpoint dive sites; (2) tracking of submersibles by the support ships; and, (3) self-contained precision navigation equipment aboard submersibles. Acoustical methods have

made a strong debut into surface ship as well as submersible navigation. Session D dealt with acoustic position-fixing problems.

Paper D1, "Method for Undersea Navi- gation and Orientation Determination, Using a Phase Compensated Line Hydro-

phone Array," by J. A. Peugh, describes a method of transmitting a band of noise or a set of single frequencies from an array of equally spaced transducers to obtain rela- tive bearing determination with an omni- directional receiving hydrophone. The angle 0 between the direction of the main lobe of the array and the axis of the array is given by sinO=rkc/360df, where • is the phase shift in degrees inserted between adjacent transducers, f is the frequency in hertz, c is the sound speed, and d is the spacing between transducers. Two arrays on the same axis on each extreme of an area

of interest can provide navigation over a limited area. Examples with details are discussed.

Paper D2, "An Acoustic Navigation System and Operating Techniques," by M.D. Pearlman, describes a system based on acoustic transponders that are state-of- the-art hardware. Transponders are inter- rogated and horizontal ranges obtained from slant ranges and transponder depths and ship or submersible depth. The trans- ceiver and computer on the craft will normally operate in an automatic mode to compute and present the fix. Operating techniques are discussed. Simple acoustic calculations are used to discuss the prac- tical capabilities and limitations of the system.

Paper D3, "An Acoustic Transponder System," by F. N. Spiess, M. S. Lough- ridge, M. S. McGehee, and D. E. Boege-

man, Jr., describes transponders that were developed at MPL and gives some at-sea results. These transponders allow for selective calling at 10.0, 10.5, or 11.0 kHz and they all reply at 12 kHz. The design is for 106 pulses delivered over a period of a year. Useful responses have been obtained to ranges of 8 miles. The shadow zones created by upward refraction (due to increase of sound speed with pressure) was verified by field tests with transponders and a towed fish.

Paper D4, "Computations for Trans- ponder Navigation," by C. D. Lowenstein, discusses initial approximate location of transponders, surveying of transponder networks, and navigation of vehicles with reference to the network. Input data are a set of range measurements from vehicle to transponder. Least-squares methods permit maximum utilization of available data.

Results of at-sea tests with the MPL deep- towed vehicle are presented. At the be- ginning, the root-mean-square uncertainty in each transponder position was 500 ft. The intermediate stage had a root-mean- square uncertainty of about 200 ft, whereas the final set of transponder locations has uncertainties of only 20-40 ft.

Paper D5, "On the Optimization of Transponder Spacing for Range-Range Navigation," by C. D. Lowenstein and J. D. Mudie, evaluates positional error in terms of range error for different trans- ponder spacings. The area within which

920 Volume 40 Number 4 1966

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