Page 15 - Spring 2009

LLOYD’S MIRROR—IMAGE INTERFERENCE EFFECTS
William M. Carey
Department of Mechanical Engineering, Boston University Boston, Massachusetts 02215
“An excellent example of the importance of experimental work based on theory for the production of clear unambiguous results.”
Introduction
On a calm day, an underwater
source of sound has its radiation
reflected from the surface of the
sea much as if it were a mirror with an
“out-of-phase” image. At moderate dis-
tances from the source of sound an
underwater receiver would detect two sig-
nals—an acoustic pressure fluctuation
due to the direct arrival of sound from the
source and a second signal from its
reflected mirror image. If the arrivals combine constructively (in-phase) a loud sound is observed and likewise when the arrivals combine destructively (out-of-phase) a fade is observed. Successive regions of loudness and fading are referred to as an image interference effect. The combination of a source near an out-of-phase reflecting surface is referred to as Lloyd’s Mirror.
The image interference effect has been central to investiga- tions in underwater acoustics and sonar throughout the last sixty years and has been simply referred to as the Lloyd’s Mirror effect. It was so well known that even the “Red Books,” (The Physics of Sound in the Sea), did not provide a reference to Lloyd. Research during World War II was conducted by the National Defense Research Committee (NDRC) that was estab- lished by Vannevar Bush under the authority of a Presidential Executive Order in 1940. The Committee later became a part of the Office of Scientific Research and Development. In 1945, the NRDC issued a twenty volume technical report summarizing this research and the “Red Books,” of high interest to underwa- ter acousticians, were the summary volumes of Division 6: Sub- Surface Warfare. These volumes were issued by Tate (1945, 1946) and reprinted by the Navy Material Command (NAV- MAT) in 1969. They comingled the significant work of many individuals and institutions, Table 1.
If identified, the Division 6 principal investigators would be recognized as the founders of underwater acoustics and
Table 1. National Defense Research Council (NRDC): Division 6: Sub-surface Warfare
signal processing that are the underpin- nings of much of our current-day endeavors. However, their individual contributions during this short period of time were unselfishly shared. Although it is difficult to be specific as to the indi- vidual contributions, nevertheless, it is beyond question that the work of the assembled scientists and engineers pre- sented in this five year time frame was both remarkable and significant. The
legacy of this war-time research is still reflected in the pres- ent-day structure of applied acoustic research and develop- ment laboratories.
The interference problem was referred to by these wartime researchers, as the image interference effect, the Lloyd Mirror Effect. With the addition of an effective sur- face reflection coefficient the method of images was found to be useful in sound transmission experiments using both continuous and impulsive sources of sound and in sonar applications such as multi-path ranging. This article will discuss first, the scientific, technical and practical aspects of the effects. Following, will be a discussion of Lloyd, the scientist and mathematician, that history seemed to have forgotten.
The Lloyd’s Mirror Effect—Image interference effect
Investigators were first concerned with the signals received at distance from explosives used to determine sound transmission characteristics. The signals received consisted of a sequence of a direct signal followed by a negative surface- reflected arrival. This group was called a poke. The reflection from the sea surface was described by an image with a change of sign and the relative amplitude of the arrivals was account- ed for by use of an effective reflection coefficient. Subsequent experiments with gated sine wave signals were described by this same method of images with the effective reflection coef- ficient for sonar frequencies (< 10 kHz) based on sea state. Young (1947) and Urick (1967) extended the treatment to include refraction, broad band signals and a realistic treat- ment of the surface reflection coefficient.
The basic approach and results of this image interference effect can be understood by the superposition of a source with strength, ρos, beneath the pressure release surface and its image strength multiplied by an effective coefficient, μ ρos. See Fig. 1. Since pressures are additive, the received pressure at R is the sum of the radiated pressure from the source and its image:
(1) The radial distances from the source and its image in the
• University of California Division of War Research w/USN Radio and Sound Laboratory
• Woods Hole Oceanographic Institution
• USN Sound Reference Laboratories w/Columbia University Division of War Research New London Laboratory
• Massachusetts Institute of Technology Underwater Sound Laboratory
14 Acoustics Today, April 2009