AN ANALYSIS OF RECORDED SOUNDS RELATING TO
THE
ASSASSINATION OF PRESIDENT JOHN F. KENNEDY*
(Prepared for
Select Committee on Assassinations, U.S. House of Representatives, by Mark R.
Weiss and Ernest Aschkenasy, Department of Computer Science, Queens College,
City University of New York, February 1979)
*Materials
submitted for this report by the committee's acoustics panel were compiled by
HSCA staff member Gary T. Cornwell.
LIST OF FIGURES
LIST OF TABLES
ACKNOWLEDGEMENT
The authors
gratefully acknowledge the support and cooperation of the New York Police
Department in providing both the facilities and personnel needed to make test
recordings of gunshot sounds. We particularly appreciate the assistance of Sgt.
Eugene McDonnell, Officer Mario Buda, and Officer Steve Baymack of the NYPD
communications division, and Lt. Frank McGee and Sgt. John O'Brien of the
firearms unit. We wish also to express our appreciation for the generous
assistance of Dr. Ali Ghozati of the Queens College Department of Computer
Science during the preparation of this report.
FOREWORD
On September 11,
1978, Dr. James Barger of Bolt Beranek and Newman, Inc. (BBN) presented to the
House Select Committee on Assassinations the results of a BBN analysis of a
Dallas Police Department (DPD) recording that had been made on November 22
1963. One of the reported findings was that, with a probability of 50 percent,
the recording contains sounds of a gunshot, or at ]east sounds as loud as a
gunshot, fired from the so-called grassy knoll area of Dealey Plaza in Dallas;
they were received by a microphone on a DPD motorcycle that was moving on Elm
Street at a speed of about 11 mph in the same direction as the Presidential
motorcade. On October 24, 1978, the committee authorized the authors of this
report to conduct an independent examination of that portion of the recording
to determine with more certainty whether the sounds in question were of such a
shot. The analysis was completed by the middle of December 1978 and described
in a public presentation to the committee on December 29, 1978. This report
describes the method and results of that analysis.
1.1 Background
On November 22,
1963, in Dallas, Tex. at the time that shots were being fired in the
assassination of President John F. Kennedy, a radio on a Dallas Police
Department (DPD) motorcycle that apparently had a stuck microphone was
transmitting sounds over channel 1 of the DPD radio network that were being
recorded at DPD headquarters. In an analysis of this recording, authorized by
the House Select Committee on Assassinations, Dr. James Barger and his
colleagues at Bolt Beranek and Newman, Inc. (BBN) isolated four groups of sound
impulses and identified them as probable sounds of gunshots, and not merely
random noise. They calculated that the statistical probabilities that these
identifications were correct were, in order of increasing time occurrence of
the sounds, 88 percent, 88 percent, 50 percent, and 75 percent. BBN found that
the probable cause of the first, second, and fourth of these groups of impulses
were noises as loud as gunshots originating in the vicinity of the sixth floor
southeast corner window of the Texas School Book Depository (TSBD) in Dealey
Plaza. The probable cause of the third group of impulses was a similarly loud
sound from the vicinity of the so-called grassy knoll area of Dealey Plaza. BBN
also found that all of the groups of sounds were picked up by the microphone on
a DPD motorcycle and that at the time of the third probable gunshot, the motorcycle
was on Elm Street in Dealey Plaza, moving at a speed of about 11 miles per hour
in the same direction as the motorcade. On October 24, 1978, the committee
authorized authors of this report to perform an independent examination of
sounds on the DPD recording to determine with a higher level of certainty if
the third group of impulses was caused by the sounds of a gunshot from the
grassy knoll.
1.2 Materials
Provided for the examination:
At the time we
began our analyses, we were provided with the following materials:
1. A high-fidelity
tape-recorded copy of the original DPD recording.
2. A high-fidelity
tape-recorded copy of the DPD tape recording that had been examined by BBN.
3. A high-fidelity
tape-recorded copy of the sounds of gunshots that were recorded by BBN during
an acoustical reconstruction experiment conducted in Dealey Plaza on August 20,
1978.
4. A topographical
survey map of Dealey Plaza, plotted at a scale of 1 inch equal to 10 feet.
5. A map of Dealey
Plaza, plotted at a scale of 1 inch equal to 40 feet, on which the locations of
microphones used in the reconstruction experiment were indicated.
6. Aerial and
ground level photographs of Dealey Plaza and relevant surrounding structures.
In addition, the
committee staff provided to us various necessary items of information, such as
the heights of buildings in Dealey Plaza, the distance to objects not shown on
the maps, the location of the DPD shooter during the BBN reconstruction
experiment and the air temperature in Dealey Plaza at the time of the
assassination and during the reconstruction experiment.
1.3 Preliminary
review of the characteristics and sources of the recorded sounds
During 1963,
communications that were transmitted on channel 1 of the DPD radio dispatching
system were recorded continuously on a Dictabelt recorder. On November 22,
1963, a microphone on a mobile transmitter that was set to channel 1 apparently
became stuck in the position at about 12:28 p.m. and for about 5 minutes
continuously transmitted sounds that it picked up. When we first listened to
this interval on the DPD recording, we found that it contained a nearly
continuous noise, with occasional speech, whistles, and clicks. Also recorded
on the Dictabelt in this interval were the sounds that BBN identified as
probable gunshots. To the ear, these sounds resembled static much more than
they did a gunshot. However, as Dr. Barger testified in September, and as we
independently verified, the equipment that was used in the DPD radio
dispatching system was not designed to handle sounds as intense as a gunshot,
and it was therefore likely to have recorded such sounds with very poor
fidelity. Consequently, we recognized that these static-like sounds could be
distorted gunshot sounds. On the other hand, such static-like sounds,
theoretically could have been generated by a number of other sources, some
acoustic, some related to electrical or mechanical disturbances in the DPD
radio transmission, reception or recording equipment. Some test more discerning
than the human ear was required to determine the probable cause of the sound
impulses.
1.4 Basic
principles and methods of analysis
To answer the basic
question, "Was the third group of recorded sounds generated by a gunshot
from the grassy knoll? With a high level of certainty, these sounds needed to
be examined for some characteristic that they would have had if they had been
generated by such a gunshot, and would not be likely to have had if they had
not been. Of the several characteristics that can be used, the most effective
and most reliable one is the sequence of delay times of the muzzle-blast
echoes.
The firing of a gun
generates a very loud, very brief explosive blast at the muzzle of the gun.
This sound, which typically lasts about five one-thousandths of a second
(0.005. seconds, or 5 milliseconds), spreads out in all directions from the
gun. If the muzzle blast strikes a wall of a structure, it will be reflected
from the surface and will move away from it in a new direction. If the muzzle
blast strikes the corner of a structure, it will be diffracted, that is, it
will spread out from the corner in many directions. These reflected and
diffracted sounds are the echoes of the muzzle blast. Like the muzzle blast,
which they closely resemble, the individual echoes are very short in duration.
The strengths of the echoes tend to diminish with time, the earliest ones,
being very loud and the later ones growing progressively weaker as they arrive
from increasingly distant locations.
The time taken for
the muzzle blast to be heard at some location depends solely on how fast the
sound travels and how far the listener is from the gun. For example, at 65 deg
F. the speed of sound is 1123 ft/sec. A listener 112.3 feet away from a gun
would hear its muzzle blast 0.1 second after the gun was fired. The time taken
for the muzzle blast echoes to be heard also depends on the speed of sound and
on the total distance each echo must travel, which is the total of the distance
from the gun to the echo-producing object and then to the listener. Since the
distance traveled by the muzzle blast to a listener must be less than the
distance traveled by one of its echoes, the bang of the muzzle blast is always
heard first. Then the echoes that are produced by the muzzle blast bouncing off
the corners and surfaces of structures are heard.
If we now assume
that the sound source (the gun) and the listener are located in a typical urban
environment, with a number of randomly spaced echo-producing structures, it is
possible to see that the pattern of sounds a listener will hear will be complex
and unique for any given pair of gun and listener locations. For example,
assuming a fixed location of a listener, the echoes that he hears and the times
at which he hears them will be related uniquely to the location of the gun,
since for each different location of the gun, even though the distances from
the listener to the various echo-producing objects are the same the distances
from these objects to each gun location are different. Consequently, the times
at which the echoes are heard will be different for each location of the gun.
Similarly, assuming a fixed location of the gun, any change in the location of
the listener will change the distances between him and the echo-producing
structures, and thus the timing of the pattern of sounds he hears. If the
listener is in motion as the muzzle blast and the various echo sounds reach
him, the times at which he hears the muzzle blast and its echoes will be
related uniquely to his location when he hears each sound.
A listener cannot
tell, from the sounds of a gunshot, when the gun was fired. He can determine
only the times that elapse between the muzzle blast and each of its echoes.
These elapsed times are called the echo-delay times. Because the echo travel
times are uniquely related to the locations of the gun and the listener, the
echo-delay times are unique to any given pair of those locations. Hence, if we
know the temperature (and thus, the speed of sound) and the location of the
echo producing structures, echo-delay times can be used to characterize the
sounds of a gunshot for any pair of shooter and listener locations.
The
"listener" that we have discussed, of course, could be either a human
ear or a microphone. If a microphone receives the sounds and they are
subsequently recorded, the recording becomes a picture of the event, not unlike
a "fingerprint," that permanently characterizes the original gun and
microphone locations.
Echo-delay times in
such recordings can be measured easily and precisely by producing a graph of
their waveforms on an oscillogram, or oscillograph. Such a graph is shown in
figure 1. The narrow peaks represent individual sounds of brief duration (that
is, impulse-sounds). The heights of the peaks correspond to the loudness of the
impulse sounds; the spacing between peaks corresponds to the time that elapses
between them. The largest of the impulse peaks is the muzzle blast. The peaks
that follow it are its individual echoes. The distance between the peak that is
identified as the muzzle blast and each peak that represents an echo is a
measure of the delay time of the echo. To convert this distance to a time
measurement, it is multiplied by the time-scale of the graph. For example, the
muzzle blast impulse in figure 1 and the sixth peak identified as an echo are
47 millimeters apart. Since the time-scale is 1 millisecond per millimeter (1
msec/mm), the measured echo-delay time is 47 milliseconds.
FIGURE 1 WAVEFORMS
OF THE SOUNDS OF A GUNSHOT
It is easy to see
how such a graph may be used for identification purposes. It provides a picture
of the complex, random spacings of the echo-delay times. When the temperature
of the air and the locations of the echo-producing objects are known, the graph
is uniquely related to a particular pair of gun and microphone locations. This
complex picture can be compared to other such graphs. If the random pattern of
echo-delay times (the spacings between peaks) matches in any two such graphs,
it may be concluded that the sounds and listener locations that produced both
graphs were the same.
Of course, it may
be that no second graph can be found that matches the first. Using the
fingerprint identification process as an analogy, if a latent fingerprint taken
from a knife found protruding from a murder victim's body is given to the FBI
for identification, it may be that no matching "known" print is on
file at FBI headquarters and that the murderer cannot be immediately
identified. Furthermore, the police may proceed to take fingerprint samples
from all of the suspects in the case and find that none match the one found on
the murder weapon. In the end, the latent fingerprint may not be identified.
Applying the analogy
to the graphs of sounds, our problem was to see if any of a number of assumed
pairs of shooter and microphone locations would produce a pattern of sounds
whose graph would match the graph of the sounds in question on the DPD tape.
Before beginning the search, we knew that, just as in fingerprint
identification cases, in the end we might find no match. If that occurred, of
course, either of two conclusions would be required: (1) The real shooter and
microphone locations could not be identified, or (2) the sounds on the tape
were not produced by a gunshot in Dealey Plaza. On the other hand, if we found
a shooter and microphone location that in combination would cause the same
unique, random pattern of echo-delay times that were contained on the DPD tape recording,
those sounds could be identified as probably being caused by such a gunshot.
For the sounds on
the DPD recording, we knew what two of the four conditions that determine
echo-delay time were at the time of the assassination. We knew what the speed
of sound was and we knew where the major echo-producing objects were (and still
are). We did not know exactly where to locate the gun, nor did we know through
which sequence of locations on Elm Street to move the microphone. Therefore, we
had to determine numerous hypothetical sequences of echo-delay times for
gunshots that may have been fired from a variety of locations on the grassy
knoll and picked up by microphones that moved through a variety of locations on
Elm Street. This was accomplished in the only practical way possible--by
predicting (i.e., mathematically calculating) the echo-delay time sequences
that would be obtained for the various locations of a gun and a microphone.
After numerous
comparisons between the echo-delay times for the sounds on the DPD recording
and various predicted patterns for assumed motorcycle and shooter locations
that did not match, a combination of motorcycle and shooter locations was found
which mathematically produced a predicted pattern that showed strong similarities
to the pattern of impulses on the DPD tape. However, to determine with a high
level of certainty if these two sequences of echo delay times, which were
derived from different data, represented the same source, it was not enough to
show that the sequences looked alike.
They had to be
shown to be alike in an objective sense, that is, by use of a method of
comparison that disregarded potentially misleading appearances. Such a method
was provided by a computation of the binary correlation coefficient of the two
sequences. The binary correlation coefficient of two sequences is a number that
is exactly 1.0 if the sequences are identical and that rapidly approaches zero
as they grow more dissimilar. As used in this analysis, the binary correlation
coefficient takes into account the number of echo-delay times in each of the
sequences and the number of echoes that coincide. Echoes in the two sequences
are said to coincide if their delay times differ by a small amount. The smaller
this amount, or "coincidence window," can be made while maintaining a
high binary correlation coefficient, the greater will be the probability that
the DPD sequence represents a gunshot from the grassy knoll.
1.5 Results of the
analysis
Two different
comparisons were made between the sequence of echo delay times on the DPD tape
and the most similar sequence of predicted echo-delay times. One of the
comparisons was between those recorded sounds that were significantly louder
than the average background noise and those predicted echoes that would have
been recorded with comparable loudness. In the other comparison, the delay
times of all of the recorded sounds and of all of the predicted echoes, up to a
total delay of 50 milliseconds from the muzzle blast, were compared. The
computed binary correlation coefficient was found to be 0.79 for the first
comparison and 0.75 for the second.
In both of the
comparisons described here, the coincidence window was set at -+1 millisecond.
That is, a documented echo-delay time and a predicted one were said to coincide
only if they were no more than 1 millisecond apart. For sequences that
correlated at levels greater than 0.7 with a coincidence window of a
millisecond. the statistical probability was 95 percent or more that the
sequences represented the same source--a sound as loud as a gunshot from the
grassy knoll. Put alternative]y, the probability that the sounds on the DPD
recording were generated by sources other than a sound as loud as a gunshot
originating from the grassy knoll is 5 percent or less.
1.6 Findings
The results of our
analysis of sounds on the DPD recording permit the following findings:
1. The recording
very probably contains the sound of a gunshot that was fired from the grassy
knoll. The probability of this event is computed to be at least 95 percent.
2. The microphone
that picked up the sounds of the probable gunshot was on Elm Street and was
moving at a speed of about 11 miles Der hour in the same direction as the
motorcade. At the time the probable gunshot was fired, the microphone was at a
point about 97 feet south of the TSBD and about 27 feet east of the southwest
corner of the building. (For both distances, the uncertainty is about +- 1
foot.)
3. The probable
gunshot was fired from a point along the east-west line of the wooden stockade
fence on the grassy knoll, about 8 feet (-+-5 feet) west of the corner of the
fence.
1.7 Outline of the
Report
The method and
results of this analysis are described in detail in the sections of the report
that follow. The sounds on the DPD recording are described in section 2.
Following in section 3, is a discussion of the nature of the problems in this
analysis and of the considerations that underlie the method of solution.
Section 4 discusses the steps that were taken to implement the procedure for
predicting echo-delay times and describes the method and results of a test of
this procedure. Section 5 discusses the methods that were used to determine and
to compare echo-delay times for the recorded and predicted sequences.
2.0
DESCRIPTION OF THE RECORDED SOUNDS
The DPD recording
contains a wide range of sounds--speech, clicks, whistles, motor noises, sirens
and even the sound of a carillon bell. Mostly, the recording contains sounds
generated during normal communications on channel 1 of the DPD radio
dispatching system. The speech transmissions usually were preceded and followed
by sharp clicks. These were keying transients, probably generated by the switch
on the transmitter microphones when they were turned on or off. Occasionally, a
transmission was attempted while another one was in progress. When this
occurred, the interference between the two transmitters usually generated a
brief whistle, known as a heterodyne tone, that immediately followed the keying
click of the oncoming microphone. At a time that the BBN analysis estimates to
have been about 12:28 p.m., a microphone on a mobile unit apparently became
stuck in the "on" position and began to transmit a continuous noise
that is believed to be the sound of a motorcycle engine. For the first 2
minutes of the stuck-microphone transmission, the sound level of this noise is
fairly constant. Occasionally, clicks and whistles can be heard through the
noise, indicating attempts by other transmitters to use the channel. At several
points, voices can be heard, but, being obscured by the noise, they cannot be
understood. At 133 seconds after the start of the stuck-microphone
transmission, the level of the noise drops by about 6 decibels (that is, to
about one-fourth of its previous level). At almost the same moment a voice can
be heard, communicating a brief but unintelligible message. This is followed
about 3 seconds later series of randomly spaced, loud clicks and pops that
lasts for at least 10 seconds. Some of the clicks occur singly, some in groups.
Only one of them is accompanied by a heterodyne whistle and by an audible but
unintelligible voice.
3.0
THE NATURE OF THE PROBLEM AND THE METHOD OF SOLUTION
3.1 Distortion of
the relative intensities of the echoes
The sounds on the
DPD recording that are thought to be those of gunshots begin about 5 seconds
after the decrease in the level of the continuous noise and last for about 8
seconds. To the ear, these sounds resemble static, not gunshots. However, the
equipment that was used in the DPD radio dispatching system in 1963 would have
distorted the sounds of gunfire. The effect would have been to compress the
peak amplitude of the sounds of the muzzle blast and of its strongest echoes,
making them only slightly louder than those of some of the weaker echoes.
Furthermore, if the microphone was on a DPD motorcycle in the motorcade, most
of the many very weak echoes of the muzzle blast would have been obscured by
the noise of the motorcycle engine (which is possibly the source of the
continuous noise on the DPD recording). Consequently, the sounds of a gunshot
would have been recorded as a sequence of very brief impulse-sounds (the muzzle
blast and its loudest echoes), only a few of which would have been larger than
the accompanying engine noise, and none of which would have sounded to the ear
like gunshots after being distorted by the limiting circuitry of the DPD radio
and recording equipment.
3.2 Waveforms of
the sounds on the DPD recording
The waveforms of
sounds in the DPD recording are shown in figure 2. The waveforms in the
bracketed region include the group of impulse-sounds that the BBN analysis
identified as a probable, gunshot from the grassy knoll. This segment of the
recording begins 144.9 seconds after the start of the stuck-microphone transmission
and lasts for 0.36 seconds. The noise thresholds shown in the figure indicate
the average peak levels of noise (mostly motorcycle noise) that can be heard
immediately before and after this segment.
FIGURE 2 WAVEFORMS
OF SOUNDS IN THE DPD RECORDING
Figure 3 shows the
bracketed region in greater detail. The narrow peaks that exceed the
thresholds, as well as many of those that do not, are the waveforms of the
impulse-sounds that may be the sounds of a gunshot. Impulse peaks that are less
that 1 millisecond apart are considered to be part of the same impulse.
Altogether, 15 impulses exceed the thresholds. Five of them occur in the first
85 milliseconds following the one that is labeled as the muzzle blast. The
remaining tone impulses occur in the 100-millisecond wide interval that begins
about 280 milliseconds after the assumed muzzle blast.
FIGURE 3 EXPANDED
GRAPH OF WAVEFORMS OF SOUNDS IN THE DPD RECORDING
3.3 Possible
sources of the impulse sounds
While it was
possible that the louder impulse noises were the distorted sounds of a gunshot,
it also is possible that they could have been generated in other ways. For
example, they could have been the sounds of misfiring of the motorcycle engine.
They could have been static-like impulse noises generated by the motorcycle's
ignition system and picked up by the transmitter. The microphone that was stuck
in the "on" position could itself have been the cause of impulses if
from time-to-time it became unstuck and turned off briefly and then immediately
turned on again. Impulse noises in the recording could also have resulted from
scratches in the dictabelt on which the recording was made. Other components of
the communication system could have been malfunctioning, producing electrical
or mechanical disturbances that would have been recorded as clicks.
3.4 Method of the
analysis
The essential
questions to be answered were: "What is the source of the impulse-sounds
in the DPD recording? Are they derived from the sounds of a gunshot that was
fired from the grassy knoll and picked up by a microphone that was moving on
Elm Street, or are they derived from one or more of the many other possible
sources?." These questions could be answered with a high degree of
certainty if the impulses could be shown to exhibit a characteristic that they
would be expected to exhibit if they had been generated by a gunshot, and would
not be likely to exhibit if they had not been. As explained in 1, such a
characteristic is found in the unique pattern of time delays of echoes that
buildings and other structures in Dealey Plaza would generate for a gunshot
fired from the grassy knoll. If the impulse noises are the distorted sounds of
a gunshot, their spacing should closely match that predicted for a shot fired
from some location on the grassy knoll and "heard" by a microphone
traveling along some path on Elm Street at 11 miles per hour. The closer the
match between the actual and the predicted sequences, the greater the
probability that the impulses are the sounds of a gunshot. If no shooter and
microphone can be found that can produce a sequence of echoes that closely
matches the sequence of impulses on the tape recording, then it would have to
be concluded that the impulses were not generated by sounds received by a
microphone moving on Elm Street from a gun fired on the grassy knoll.
The procedure for
determining the probable cause of the specified group of impulses on the DPD
recording thus consisted of three steps. First was to calculate the pattern of
echo delays that would be produced by a gunshot from a variety of locations on
the grassy knoll and recorded by a microphone moving along a variety of paths
on Elm Street. Then, select the sequence of predicted echoes that most closely
matched the actual recorded sequence of impulses. Finally, compute the
probability that impulse sounds generated by sources other than the predicted
gunshot could occur by chance in a sequence that would match the selected echo
sequence as closely as did the actual DPD recording.
4.0
IMPLEMENTATION OF THE ANALYSIS
4.1 Preliminary
considerations
The implementation
of the three-step procedure of the analysis required the consideration of a
number of questions. Each of these affected either the results of the analysis
or the method by which the required echo-delay time sequences were obtained.
4.1.1 Source of the
gunshot sounds
If a gun was fired
from the grassy knoll during the assassination, the would-be assassin
reasonably could have used either a rifle or a pistol, since the target would
have been less than 150 feet away. Since rifles typically fire bullets that travel
faster than the speed of sound, the firing of it rifle generates two intermixed
echo sequences composed of the echoes of the muzzle blast and the echoes of the
continuously generated shock wave that is created by a bullet in supersonic
flight. On the other hand, most pistol bullets do not fly at supersonic speeds.
A pistol that fires a subsonic bullet generates only the set of echoes of the
muzzle blast. Since we did not know what type of gun, if any, had actually been
used on November 22, 1963, we sought only to compare the DPD tape with
predicted sequences of echoes of muzzle blasts which would have been present
regardless of the type of weapon fired.
*The
DPD recording does contain a series of impulses that precede the large impulse
ultimately determined to be the muzzle blast. The probability that these
earlier impulses were the sounds of supersonic shock wave was discussed by Dr.
Barger in his testimony before the committee on Dec. 29, 1978. See Vol. V of
the hearings before the select committee, 94th Cong. 2d session (Washington,
D.C.: U.S. Government Printing Office, 1979).
4.1.2 Placement of
the gun on the grassy knoll
The BBN analysis
indicated that the gun was in the vicinity of the grassy knoll. During the
acoustic reconstruction experiment that was conducted by BBN in Dealey Plaza on
August 20, 1978, shots were fired from behind the wooden stockade fence on the
grassy knoll. This location was consistent with available eyewitness and ear
witness testimony. It was a reasonable one since it afforded good visibility of
Elm Street while providing good cover for the shooter of a gun. At any other
location on the grassy knoll either the visibility or the cover would have been
substantially poorer. However, it is uncertain exactly where a shooter would
have stood behind the fence, since equally good locations can be found up to 25
feet along the fence either north or west of its corner.
4.1.3 Placement of
the microphone on Elm Street
The BBN analysis
placed the stuck microphone on Elm Street in the vicinity of the fourth
microphone in the third array of microphones that were set up in Dealey Plaza
during the acoustic reconstruction experiment. As illustrated in figure 4, the
microphones were located in the center of the street at points 18 feet apart
along the route of the Presidential motorcade, from the intersection of Houston
and Main Streets to the location of the Presidential limousine on Elm Street in
Zapruder frame 312. The sounds of a gunshot from the grassy knoll received by
each of these microphones were recorded during the experiment. Later, BBN
determined the degree of match between the recordings from each of these
microphones and the impulse noises on the DPD recording by calculating their
binary correlation coefficients.
A coincidence
window of _+_ 6 milliseconds was used for these comparisons. Only one of the 36
comparisons yielded a correlation coefficient greater than 0.5 when compared
with the segment of the DPD tape that is here at issue. That one--for the
sounds received by microphone 4 in array 3--was at a level of 0.8, indicating a
strong similarity between the echo sequence that was heard at that test
location in Dealey Plaza and the impulse sequence on the DPD recording. The low
values of the binary correlation coefficients that were calculated for all of
the other microphones indicate that there is no other microphone location
either on Elm Street or on Houston Street at which a sequence of echoes caused
by a shot from the grassy knoll could be heard that was even moderately similar
to the sequence of impulses on the DPD recording.
FIGURE 4 MICROPHONE
LOCATIONS AT THE DEALEY PLAZA
It was therefore
clear that for the purpose of analysis the microphone location in Dealey Plaza
for which echo sequences had to be obtained was in the vicinity of microphone 4
of array 3. This region extends along Elm Street from halfway between
microphones 3 and 4 to halfway between microphones 4 and 5, and from curb to
curb (since the presumed motorcycle with the stuck microphone could be anywhere
to the right or left of the center of the street).
4.1.4 Selection of
the coincidence window
To compare
sequences of impulses and echoes by use of the binary correlation coefficient,
it was necessary first to determine how many echoes coincided with impulses.
Ideally, if the microphones that were used in the acoustic reconstruction
experiment could have been spaced very closely along the route of the
motorcade, say, 1 foot apart, and spread from curb to curb, impulses and echoes
that were within 1 millisecond of one another could have been considered
coincident. For practical reasons, the microphones were located in the middle
of the street and spaced 18 feet apart. Also, only one of many possible shooter
locations was used. To take into account these practicalities, the coincidence
window for BBN's analysis was made -+6 milliseconds. If a window of -+ 1
millisecond had been used, there would have been few points of coincidence in
any comparison, and all of the calculated binary correlation coefficients would
have been small, since the chances would have been small that a microphone and
a shooter would (have) been arbitrarily located in precisely the correct positions
to receive a sequence of echoes that. coincided with the sequence of impulses
to within 1 millisecond. By increasing the coincidence window to +6
milliseconds, the number of coincident impulses and echoes was increased.
However, so was the possibility that an impulse generated by a source other
than a gunshot would appear to coincide with an echo. The major consequence of
this was the value of 50 percent computed as the statistical probability that
the impulses under examination were caused by the sounds of a gunshot.
To increase the
certainty in our findings above a 50-percent level, we had to be able to reduce
the coincidence window to as low a value as possible, preferably to -+-1
millisecond or less. Theoretically, this could be accomplished by placing
microphones l foot apart in the region of interest and conducting additional
test firings in Dealey Plaza from various locations on the grassy knoll With
respect to the microphone location problem along the relevant area on the
street would be 720 square feet. Therefore, if, as in the BBN acoustic
reconstruction experiment, microphones were placed in arrays of 12 each, a
total of 60 arrays would be required for each position of a gun fired on the
grassy knoll. Clearly, this approach was impractical.
4.1.5 Prediction of
echo sequences
The only practical
way to obtain the needed echo sequence was to predict them analytically. Using
fundamental principles of acoustics, it was possible to compute the time it
would take for the sound of a muzzle blast to travel from a gun at any assumed
point on the grassy knoll to a microphone at any assumed point on Elm Street.
Knowing where the echo-producing objects were in Dealey Plaza, it was also
possible to compute the time it would take for echoes of the muzzle blast to
travel from the gun to the microphone. Subtracting the muzzle-blast travel time
from the echo travel times yielded the required sequence of echo-delay times.
The principles of
acoustics that underlie this approach are described in detail in BBN Report.
No. 3497 that was submitted to the committee in January 1979.* The essential
principles can be summarized as follows:
1. Most sounds
spread out in all directions from the source of the sound.
2. If the medium
(in this case, air) through which sound travels is uniform, sound will travel
in straight lines from the source and the same constant velocity in all
directions of travel.
3. The time taken
for sound to travel from one point to another can be computed by dividing the
distance between the points by the speed of sound. For example, at a speed of
1,100 feet per second, it will take 0.5 second for sound to travel a distance
of 550 feet. Conversely, the distance traveled by a sound can be computed by
multiplying the travel time by the speed of sound.
4. Sound traveling
through air will reflect from the surfaces and diffract from the corners of
structures such as buildings, walls and columns.
4.2 Information
needed to predict echo-delay sequences
Before the echo
travel times could be calculated, it was necessary to determine three things:
(1) Which objects in Dealey Plaza would produce echoes in the region of
interest, on Elm Street for a gun fired from the vicinity of the grassy knoll;
(2) how far these objects were from the locations of the gun and of the
microphone; and (3) what was the speed of sound under the conditions for which
the echo travel times were to be predicted. When the required information had
been obtained, it was used first to determine the accuracy of the echo
procedure. Then it was used to predict echoes for comparison with the impulses
in the DPD recording.
4.2.1
Identification of echo-producing objects
The objects in
Dealey Plaza that would generate relevant echoes were identified with the aid
of a topographical survey map of the plaza that was drawn to a scale of 1 inch
equal to 10 feet. Most of these objects were corners of buildings or of walls
that, as illustrated in figure 5, produced muzzle blast echoes in the selected
region on Elm Street by diffracting the incident sound of a muzzle blast that
was generated in the vicinity of the grassy knoll. Two of the objects, the wall
of the DCRB and the curved wall at the reflecting pool, produced echoes by
reflecting such a sound. In all, we were able to identify 22 objects that would
generate echoes of sufficient strength that, they would have been recorded on
the Dictabelt recording. (See table 1.)
4.2.2 Measurement
of distances in Dealey Plaza
The distances of
the echo-producing objects from positions of a gun and a microphone were
determined by direct measurement on the survey map. By comparing the known
widths of buildings in Dealey Plaza with measurements made on the map, we found
the distances measured on the map to be accurate to about 0.5 foot. We measured
distances on the map in millimeters, to the nearest half-millimeter. This
simplified the making of measurements by providing a decimal
FIGURE 5 PATHS OF
THREE MUZZLE BLAST ECHOES
scale. To simplify
the calculation of the travel time of the echoes, we converted the speed of
sound to an equivalent value for map distances that were measured in
millimeters. For example, a speed of sound of 1,123 feet per second was
converted to 2,852 millimeters per second for map measurements made in
millimeters.
4.2.3 The speed of
sound
The speed of sound
in air is primarily a function of the temperature of the air. At a temperature
of 65(deg) Fahrenheit, it is 1,123 feet per second, and at 90(deg) Fahrenheit
it is 1,150 feet per second. To a first order approximation, in this
temperature range the speed of sound increases at a rate of 1 foot per second
per degree Fahrenheit. By comparison, humidity has a negligible effect on the
speed of sound in air. Similarly, small variations in the temperature at
different locations in Dealey Plaza would have a negligible effect on the
average speed of sound over the path lengths of the echoes.
According to
records of the weather bureau in Dallas, as obtained by the committee staff,
(See addendum A to the acoustics reports) the temperature in Dallas at 12:30
p.m. on November 22, 1963 was 65(deg) Fahrenheit. This was substantially
confirmed by a photograph that was taken in Dealey Plaza at about that time. In
it, a sign on top of the TSBD can be seen on which the time is indicated as
12:40 and the temperature in Dealey Plaza as 68 (degree) Fahrenheit. Even if
the temperature that was supplied by the weather bureau varied from the
temperature in Dealey Plaza by 3 (degree) Fahrenheit, the resulting error of 3
feet per second is less than 0.27 percent of the speed of sound at 65 (degree)
Fahrenheit. For most of the echoes, the resulting error in the computed
echo-delay time would be less than 0.25 millisecond. Even for the echoes that
travel the longest echo paths, the error would be less than 1 millisecond. In
either case, the error is within the accuracy required for the echo prediction
procedure. As is explained later in this report, temperature differences up to 10
(deg) Fahrenheit would have had negligible effect on the final results and
would not substantially have changed the final conclusion nor the degree of
confidence (the final statistical probability) that can be appropriately
assigned to it.
Wind also will
affect the speed of sound, increasing or decreasing it by an amount that
depends on the speed of the wind and on the angle between the direction of the
wind and the direction the sound travels. However, the delay time of an echo,
which is determined by subtracting the muzzle blast travel time from the echo
travel time, will be affected by wind only to the extent that the wind affects
the echo and muzzle blast travel times differently. This in turn depends on the
difference between the direction of the echo path and the direction of the
direct muzzle blast path. For a gunshot fired from the grassy knoll and heard
on Elm Street, the travel of most echoes is in approximately the same direction
as the directly received muzzle blast. Consequently, the effect of wind on the
delay times of these echoes is comparatively small, becoming significant only
for wind speeds greater than 40 miles per hour. The weather bureau recorded
winds in Dallas on November 1963, as ranging only between 13 knots and 17
knots, which is roughly equal to 15 to 20 miles per hour. (The actual recordings made at Dallas Love
Field were 13 knots at 11:55 a.m., 13 knots at 12:30 p.m., and 17 knots at 1:00
p.m. See addendum B to the acoustics report. )
4.3 Accuracy of the
echo prediction procedure
Before proceeding
to predict sequences of echoes for comparison with the sequence of impulses on
the DPD recording, the accuracy of the echo prediction procedure was tested.
Given the estimated accuracy of the map, we expected to be able to predict echo-delay
times to within - + 1 millisecond for specified locations of a gun and a
microphone. However, it was essential to verify that this accuracy would be
achieved in practice and that the identified echo-producing objects would
generate significant echoes in the region of interest on Elm Street.
To test the
procedure, we predicted the delay times of the echoes that would be received by
a microphone at the location of microphone 4 of array 3, as shown in figure 5,
for a shot fired from the grassy knoll by the DPD shooter during the acoustic
reconstruction experiment. We then compared the predicted echo-delay times to
echo-delay times actually recorded on the BBN tape recording of the shot that
was fired by the DPD shooter. At the time that the test shot was fired, the
temperature in Dealey Plaza was approximately 90(deg) Fahrenheit. Accordingly,
the value used for the speed of sound was 1,150 feet per second. As discussed
in section 4.1.5, the echo-delay time is computed by subtracting the muzzle
blast travel time (185.2 msec.) from the echo travel time. The muzzle blast
travel time is obtained by dividing the distance between the gun and the
microphone in Dealey Plaza (213 feet) by the speed of sound.
For echoes produced
at the corners of structures, the measurement procedure was simple and direct.
For example, the path of echo 2 in figure 5 consisted of two segments. As
measured on the map, the segment. from the shooter to the diffraction point was
499 millimeters and from that point to the microphone was 92 millimeters. The
total path length, 591 millimeters, when divided by the sound-speed constant
(2921 mm/sec) yielded an echo travel time of 0.2024 second (202.4 msec).
Subtracting the muzzle blast travel time from the echo travel time yielded an
echo-delay time of 17.2 milliseconds.
For an echo
produced by a specular reflection, it was necessary first to locate the point
at which the reflection would occur. Such reflections occur at that point on an
echo-producing surface at which the total length of the echo path to that
surface is a minimum. At that point, the reflecting surface will be tangent to
an ellipse for which the locations of the gun and the microphone are the loci
and the total length of the echo path is equal to the sum of the radii. The required
ellipse was easily generated by the following procedure. First, a
non-extensible string was cut to a length greater than the probable length of
the echo path on the topographical map. One end of the string was tied to a pin
at the location of the gun and a portion of the string near its other end was
wrapped tightly around a pin at the location of the microphone. The string was
then pulled toward the reflecting surface by the point of a pencil. With the
string drawn taut, the pencil was moved so that its point drew an arc on the
map in the region of the line that represented the reflecting surface. The
length of the string was then adjusted until the arc was just tangent to the
line. The point at which the arc touched the line was the desired point of
reflection. The path from the gun to the point of reflection and then to the
microphone (the echo path) was then measured. The total distance of the echo
path divided by the speed of sound was the echo travel time. Subtracting from
it the muzzle blast travel time yielded the echo-delay time.
TABLE 1.-- List of
structures in Dealey Plaza that would have produced echoes of sufficient
strength to have been recorded on the DPD tape
Object No.
Identification
[1] Wall
"A" is a concrete wall on the north side of Elm St. that runs in an
east-west direction. Corners 1 and 2 are at the east end of the wall. The
direction of the wall changes from east to northeast at corner 1, and from
northeast to north at corner 2.
[2] Column
"A" is a concrete column on the north side of Elm St. near the
intersection with Houston St.
[3] Wall
"B" is a concrete wall on the south side of Elm St. near the
reflecting pool. It runs in a generally north-south direction. Corners 1 and 2
are at the northern end of the wall. The direction of the wall changes from
north to northeast at corner 1 and from northeast to east at corner 2.
[4] Column
"B" is a concrete column on the south side of Elm St., at the
northern end of Wall "B."
TABLE 2.--List of
echo paths used in the predictions of echo-delay times
Echo producing
objects
Path No.:
(Identification numbers)
TABLE 3.--MEASURED
AND PREDICTED DELAY TIMES OF ECHOES FOR A GUNSHOT FIRED ON AUG. 20. 1978
[in milliseconds]
Echo-delay
time [1]
Echo
path |
travel
time |
Predicted
|
Measured
|
Deviation
|
1
|
192.3
|
7.0
|
7.3
|
0.3
|
2
|
196.0
|
10.8
|
11.2
|
.4
|
3
|
198.6
|
13.4
|
13.1
|
.3
|
4
|
201.7
|
16.5
|
16.9
|
.4
|
5
|
202.4
|
17.2
|
16.9
|
.3
|
6
|
213.0
|
27.8
|
28.3
|
.5
|
7
|
213.0
|
27.8
|
29.8
|
2.0
|
8
|
215.4
|
30.1
|
29.8
|
.3
|
9
|
218.1
|
32.9
|
32.9
|
0
|
10
|
228.4
|
43.2
|
42.3
|
1.1
|
11
|
229.4
|
44.74
|
5.6
|
.9
|
12
|
232.5
|
52.35
|
2.9
|
.6
|
13
|
243.4
|
58.2
|
60.0
|
1.8
|
14
|
252.7
|
67.5
|
68.3
|
.8
|
15
|
259.9
|
74.7
|
76.9
|
2.5
|
16
|
267.1
|
81.9
|
82.5
|
.6
|
17
|
267.4
|
82.2
|
83.1
|
.9
|
18
|
451.6
|
266.7
|
266.6
|
.1
|
19
|
455.0
|
269.8
|
269.2
|
.6
|
20
|
458.1
|
272.9
|
272.2
|
.7
|
21
|
469.2
|
284.0
|
282.3
|
1.7
|
22
|
482.8
|
297.6
|
297.7
|
.1
|
23
|
482.8
|
297.6
|
297.7
|
.1
|
24
|
487.2
|
302.0
|
303.2
|
1.2
|
25
|
497.8
|
312.6
|
313.0
|
.4
|
26
|
541.3
|
356.1
|
354.0
|
2.1
|
[1] For the
calculated locations of the gun and the microphone, the muzzle blast travel
time is computed to be 185.2 ms.
Using the methods
described above, 96 echo paths were defined for echo-producing objects."'
For some of these paths, the muzzle blast sound bounced on more than one
echo-producing object. The echo-producing objects and echo paths are listed in
tables 1 and 2. The travel times and the delay times for the predicted echoes
are listed in table 3. Also listed are the echo-delay times determined by
analysis of the time waveforms of the sounds received at microphone 4 of array
3 for the shot fired by the DPD shooter from the grassy knoll. These waveforms,
which are shown in figure 6, were obtained by playing back the recording of the
sounds that were picked up by the microphone, modifying the reproduced signal
so as to approximate the effect that a microphone of the type used by the DPD
in 1963 would have had on the signal, and then graphing the resulting signal. A
60-Hz tone that was recorded in one segment of the recording made during the
testing in August 1978 made it possible to calibrate the time scale of the
graph at 1 millisecond per millimeter. The first waveform appearing in the
graph, the large peak at the left-hand side, corresponds to the supersonic
shockwave of the rifle bullet. The second large peak is the waveform of the
muzzle blast. Following it, with generally diminishing heights, are the
waveforms of the echoes of the muzzle blast. The delay time of each echo was
determined by direct measurement of the distance from the leading edge of the
muzzle blast waveform to that of the echo. The numbered peaks shown in this
figure correspond to the predicted echoes identified in table 3.
The deviations
between the predicted and measured echo-delay times listed in table 3 were in
part due to small errors in the locations of the gun and the microphone. The
microphone location was determined from a map of Dealey Plaza that showed where
microphones were to be placed during the reconstruction experiment. However,
the scale of the map, 1 inch equal to 40 feet, limited the measurement accuracy
to about plus or minus 2 feet. Therefore, the actual location of the microphone
may have deviated from the indicated one by a foot or two. Similarly, there
were no measurements taken of the exact location where the DPD shooter stood as
he fired each shot from the grassy knoll. Consequently, it was likely that the
gun and the microphone locations that were used for the echo-delay time
predictions were slightly in error and that if these positions were adjusted
correctly, the resulting predictions would be closer to the measured echo-delay
time.
*At
the time of the presentation of our findings on Dec. 28, 1978 22 echo paths had
be defined. After that date, four additional paths were defined.
FIGURE 6 FILTERED
WAVEFORMS OF GUNSHOT SOUNDS RECEIVED AT MICROPHONE 4 OF ARRAY 3
An analysis of the
data listed in table 3 shows that the assumed locations were sufficiently
accurate for the purpose of this test. The average absolute difference between
the predicted and measured echo delay times was 0.8 millisecond. The standard
deviation of predicted delay times about this average was 0.7 millisecond.
These results are well within the accuracy required of the echo prediction
procedure.
5.0
COMPARISON OF THE SEQUENCE OF IMPULSES ON THE DPD RECORDING WITH SEQUENCES OF
PREDICTED ECHOES
5.1 Prediction of
echoes for November 22, 1963
Using the
techniques described in section 4, we predicted echoes and echo-delay times for
gunshot sounds that would have been heard in Dealey Plaza at 12:30 p.m. on
November 22, 1963. The predictions were made given the following conditions:
(1) The air temperature was 65(deg)F (with a possible error of 3(deg )F); (2)
the gun was somewhere along the wooden stockade fence on the grassy knoll; (3)
the microphone was somewhere in the region of interest on Elm Street (see
section 4.1.3) and moving with the motorcade at a speed of about 11 miles per
hour; and (4) the echo-producing objects were the same as those identified in
table 1.
The procedure that
was used to predict echoes required a few more steps than the method described
in section 4. Since the conditions required the microphone to be moving on Elm
Street at a speed of 11 miles per hour, the location of the microphone on the
map had to be moved in a similar manner. First, a location was specified on the
map at which the microphone received the muzzle blast. Then, the microphone was
moved along a path corresponding to the path it would have traveled on Elm
Street during the time it received all of the predicted muzzle blast echoes.
The location of the microphone at the time it would have received each
particular echo was determined by calculating the distance the microphone would
have moved from the initial position at a constant speed of 11 miles per hour
during an interval equal to the echo travel time. Small deviations about this
estimated distance (for example, - +1 millimeter) did not materially affect the
predicted echo travel time. The predicted echo-delay times were then obtained
by the procedure described in section 4.
5.2 Correction of
time delay measurements.
The delay times of the
impulse sounds on the DPD recording were measured directly from a graph of the
sequence of impulse waveforms, such as the one shown in figure 3. To simplify
the measurement of time intervals, the graph was plotted with a time scale of 1
millisecond per millimeter (1 msec/mm). However, before the measurements could
be used, they had to be multiplied by a time-correction factor to correct for
an error in the speed of the DPD Dictabelt. machine. As was shown in the BBN
analysis, the DPD recorder was running slow at the time the recording was made.
Consequently, when the recording is played back at the faster, correct speed,
the recorded impulse sounds will be heard closer together than they actually
were at the time the recording was made. This error could be corrected by
multiplying the time intervals measured on the graph by a time-correction
factor. The BBN analysis showed that between 12:22 p.m. and 12:37 p.m., the
average speed of the recorder was 0.95 of correct speed. The actual speed at
any time during this interval could have been from 0.94 to 0.96 of true speed.
Accordingly, the time-correction factor could range from 1.04 to 1.06.
An adjustment in
the measurement of impulse delay times would also be necessary if the
temperature in Dealey Plaza at, 12:30 p.m. on November 22, 1963, was not 65 F,
as was initially assumed. The computed delay time of each predicted echo would
be in error by about 0.1 percent for each 1 F difference between the true
temperature and the assumed value of 65 F. The effect on the predicted echoes
would be to scale their spacing from what they should be. For example, if the
temperature was more that 65 F, the computed echoes would be spaced more widely
than they should be. Since it was not likely that the assumed temperature differed
from the true temperature by more that 10 F, the factor for correcting
temperature errors would range only from 0.99 to 1.01. Assuming that the
differences in temperature and recorder speed occurred in such a way as to
compound on another, the combined factor that would correct for both recorder
speed and temperature at the same time could range from 1.03 to 1.07. Because
we knew that the range of the correction was 1.03 to 1.07, theoretically we
could use any value between 1.03 and 1.07 to adjust the measured time intervals
between the impulses on the DPD recording.
Because any value
between 1.03 and 1.07 was theoretically valid, it was permissible to choose the
value between those livits that created the best match between the impulse and
echo sequences. By fitting the DPD tape recorded impulse sequence to our
predicted echo sequences, we found that a time-correction factor of 1.043 gave
the best match, and we therefore used that factor.
TABLE 4.--MEASURED
DELAY TIMES OF IMPULSES AND PREDICTED DELAY TIMES OF GUNSHOT ECHOES FOR NOV.
22, 1963. [in milliseconds]
Echo
path |
Echo
travel time |
Echo
delay time |
Impulse
delay time |
Deviation
|
1
|
202.4
|
6.5
|
6.3
|
0.2
|
2
|
206.8
|
10.9
|
10.5
|
.4
|
3
|
211.0
|
15.1
|
14.7
|
.4
|
4
|
214.7
|
18.8
|
19.3
|
.5
|
5
|
217.0
|
21.1
|
20.1
|
1.0
|
6
|
224.3
|
28.4
|
27.4
|
1.0
|
7
|
225.2
|
29.3
|
30.3
|
1.0
|
8
|
227.1
|
31.2
|
31.6.
|
4
|
9
|
230.6
|
34.7
|
34.1
|
.6
|
10
|
244.1
|
48.2
|
48.7
|
.5
|
11
|
241.5
|
45.6
|
45.4
|
.2
|
12
|
250.3
|
54.4
|
54.2
|
.2
|
13
|
255.2
|
59.3
|
59.7
|
.4
|
14
|
266.0
|
70.1
|
69.4
|
.7
|
15
|
273.4
|
77.5
|
77.4
|
.1
|
16
|
281.8
|
85.9
|
85.3
|
.6
|
17
|
276.7
|
80.8
|
80.2
|
.6
|
18
|
473.9
|
278.0
|
278.6
|
.6
|
19
|
479.8
|
283.9
|
283.7
|
.2
|
20
|
479.8
|
283.9
|
283.7
|
.2
|
21
|
489.1
|
293.9
|
292.1
|
1.1
|
22
|
506.8
|
310.9
|
310.5
|
.4
|
23
|
507.9
|
312.0
|
312.4
|
.4
|
24
|
509.6
|
313.7
|
313.1
|
.6
|
25
|
524.0
|
328.1
|
327.5
|
.6
|
26
|
565.0
|
369.1
|
369.2
|
.1
|
[1] For the
calculated locations of the gun and the microphone, the muzzle blast travel
time is computed to be 195.9 ms.
5.3 Comparison of
the impulse and echo sequences
The sequence of
predicted echo-delay times that best matched the sequence of impulse-delay
times, computed as described above, is listed in table 4. The numbered peaks
shown in figure 7 correspond to the predicted echoes identified in table 4. The
average absolute difference between the impulse-delay times and the
corresponding echo-delay times is 0.5 millisecond, and the standard deviation
of impulse-delay times about this average is 0.3 millisecond.
The location of the
gun and the path of the microphone for which these predicted echoes were
obtained are shown in figure 8. The microphone is initially located 97 feet
south of the TSBD. and 27 feet east of the southwest corner of the TSBD. The
path of the microphone, as it received the muzzle blast and its echoes, extends
for about 6 feet along Elm Street. The uncertainty in the initial position is
+/- 1 foot, which corresponds to the accuracy of measurements made on the
topographical survey map. The gun is located about 8 feet to the left of the
corner of the wooden stockade fence on the grassy knoll. If the gun is moved
along the fence from this location, the delay times of the muzzle blast echoes
changes. However, for movements up to +/- 5 feet, these changes can be reduced to
less than 1 millisecond by making a small adjustment in the initial location of
the microphone.
FIGURE 7 IMPULSES
ON THE DPD RECORDING ASSOCIATED WITH ECHOES
FIGURE 8 LOCATION
OF THE GUN AND PATH OF THE MICROPHONE COMPUTED FOR NOVEMBER 22, 1963
The data in table 4
suggest that the sequence of impulses on the DPD recording is very similar to
the sequence of predicted echoes. A visual comparison indicates that almost all
of the impulses and echoes coincide within a window of +/-1 millisecond.
However, such an examination can be deceptive. It does not take into account the
impulses that do not coincide with echoes, or the echoes that are not matched
by impulses of even minimal amplitude. For these reasons, a more appropriate
method of comparison was to compute the binary correlation coefficient of the
sequences.
5.4 Factors
affecting the selection of impulses and echoes for correlation
Ideally, a
correlation of the impulses and the predicted echoes would have included all of
the impulses evident in the waveforms of figure 7 and all of the predicted
echoes. However, some of the impulses must have represented components of the
background noise. To minimize the number of noise impulses that might be
included in the correlation calculation, only those impulses that were greater
than the average peak level of the background noise were counted. This required
limiting the predicted echoes that were included in the correlation calculation
to those that, would have been recorded at a level above that of the background
noise. To identify these echoes and impulses, it was necessary to consider,
first, the relative strengths of predicted echoes near the microphone, and then
the way in which the DPD radio dispatching system would have altered both the
relative strengths of the echoes as recorded and the recorded level of the
background noise.
5.4.1 Relative
strengths of echoes near the microphone location.
The relative
strengths of the predicted echoes at locations along the path traveled by the
microphone would be similar to those of the actual echoes of a muzzle blast
that were recorded during the acoustical reconstruction experiment at the
nearby location of microphone, 4 in array 3 (see fig. 5). The strengths of
echoes received at these nearby locations would not differ by more than a few
decibels. Therefore, the relative strengths of the predicted echoes in the
vicinity of the moving microphone could be taken to be the same as those
received by microphone 4.
5.4.2 Effects of
the DPD radio dispatching system on the relative strengths of recorded echoes.
The DPD radio
dispatching system contained a circuit that would have greatly affected the
relative strengths of the recorded echoes of a muzzle blast. This circuit, the
automatic gain control (AGC), limited the range of variations in the levels of
signals by reducing the levels of received signals when they were too strong
and increasing their levels when they were, too weak. It responded very rapidly
to a sudden increase in the level of a signal, but comparatively slowly to q,
sudden reduction in a signal level. Consequently, the response of the AGC to
the sound of a muzzle blast would greatly reduce the recorded levels of echoes
and background noise received shortly afterward. Progressively during the next
100 milliseconds, the AGE would allow the recorded levels of received signals
to increase until full amplification was finally restored. The effect on the
predicted echoes would be to make the recorded levels of late-arriving echoes
very nearly the same as those of the early ones. Concurrently, the recorded
background noise would gradually rise to its level before the muzzle blast was
received.
A different but
also significant effect on the relative strengths of the recorded echoes would
have been caused by the motorcycle windshield. On the DPD motorcycles, the
microphone was usually mounted on a bar directly behind the windshield. Sounds
arriving from the front of the motorcycle would have diffracted around the
windshield and in doing so would have lost strength. As determined by
experiment, the windshield of a 1960's Harley Davidson motorcycle attenuated
gunshot sounds received from in front of the motorcycle by from 3 decibels to 6
decibels. The amount of attenuation depended on how close the microphone was to
the windshield. Obviously, sounds received from the sides and rear of the
motorcycle would not be affected by the windshield.
5.5 Correlations of
impulse and echo sequences
The selection of
impulses for the calculation of the binary correlation coefficient depends
directly on the noise level to which the heights of the impulses are compared.
This level can be set, as in figure 2, at the average peak level of the
recorded noise immediately adjacent to the recorded impulses. This approach,
however, presumes that the noise level is the same during the impulse segment
as it is in the adjacent segments of the recording. As was discussed above, the
level of the noise recorded during the first 50 milliseconds following a muzzle
blast will be greatly reduced. Consequently, an alternative would be
correspondingly to lower the level to which the impulses are compared during
this 50-millisecond period.
Both approaches to
setting the amplitude comparison level were used, each in a separate
calculation of the binary correlation coefficient. For the first calculation,
the amplitude comparison level was set as in figure 2. Taking all of the
factors discussed in section 5.4 into account, we found that 13 gunshot sounds
(the muzzle blast and 12 of the predicted echoes) would have been loud enough
to have been recorded at a level above the background noise. Eleven of these
sounds coincided, within a millisecond window, with impulses that exceeded the
amplitude comparison level. Including the leading impulse, which was identified
as the muzzle blast, a total of 15 impulses exceeded this level. The binary
correlation coefficient was calculated as the number of gunshot sounds and
impulses that coincided (11) divided by the square root of the product of the
number of selected impulses (15) and the number of selected gunshot sounds
(13). For these data, the binary correlation coefficient was calculated to be
0.79..
For the second
calculation of the binary correlation coefficient, the delay time range over
which impulses and echoes were compared was limited to the first 50
milliseconds following the muzzle blast, since this was the range in which the
AGC would have had greatest effect. (It is also the range in which most of the
echoes arriving from the front of the motorcycle occurred.) In this
calculation, the amplitude comparison level was reduced to one-fourth of its
value during the previous calculation, which placed it at a level just above
that of very small peaks among the waveforms of the recorded impulses. Eighteen
impulses exceeded this level. So would have the muzzle blast and all echoes that
were predicted to occur in the delay time range up to 50 milliseconds. Eleven
of these sounds coincided, within +-1 millisecond, with one or another of the
selected impulses. These coincident impulses and echoes, 12 gunshot. sounds,
and 18 impulses-resulted in a computed binary correlation coefficient of 0.75.
5.6 The probability
that the recorded impulses are not gunshot sounds.
The high degree of
correlation between the impulse and echo sequences does not preclude the
possibility that the impulses were not the sounds of a gunshot. It is
conceivable that a sequence of impulse sounds, derived from non-gunshot
sources, was generated with time spacings that, by chance, corresponded within
one one-thousandth of a second to those of echoes of a gunshot fired from the
grassy knoll. However, the probability of such a chance occurrence is about 5
percent (See the BBN report No. 3947).
This calculation represents a highly conservative point of view, since
it assumes that impulses can occur only in the two intervals in which echoes
were observed to occur, these being the echo-delay range from 0 to 85
milliseconds and the range from 275 to 370 milliseconds. However, If the
impulses in the DPD recording were not the echoes of a gunshot, they could also
have occurred in the 190-millisecond time-span that separated these two
intervals. Taking this time span into account, the probability becomes
considerably less than 5 percent that the match between the recorded impulses
and the predicted echoes occurred by chance. Thus, the probability is 95
percent or more that the impulses and echoes have the same source a gunshot, or
a sound at least as sound as a gunshot, from the grassy knoll. Stated
differently, the odds are less than 1 in 20 that the impulses and echoes were
not caused by a gunshot from the grassy knoll, and at least 20 to 1 that they
were.