Report No. 4034
Analysis of Earwitness Reports Relating to the Assassination of President John F. Kennedy

D.M. Green
January 1979

Prepared for:
Select Committee on Assassinations
Bolt Beranek and Newman Inc.
50 Moulton Street
Cambridge, MA 02138




The analysis of witness reports comprised (1) an examination of two compilations of testimony given by witnesses present in Dealey Plaza on November 22, 1963, (2) an analysis of how the sounds of gunfire in Dealey Plaza would be perceived by witnesses located at different areas in the Plaza, and (3) the reports of trained listeners who were present during the acoustical reconstruction on August 20, 1978. The two compilations examined were those by J. Thompson, in his book, Six Seconds in Dallas, and by members of the staff of the House Select Committee on Assassinations.

All earwitness reports, whether of those present in Dealey Plaza in 1963 or of the experienced listeners in 1978, must be examined with an understanding of the characteristic acoustical behavior of gunfire in a reverberant space. Section 2 of this report explains how listeners can misjudge the source and number of shots in such a space. Section 3 reports the analysis of the two compilations mentioned above; Sec. 4 details the observations of trained listeners stationed in the Plaza during the acoustical reconstruction.


The nature of gunfire is such that three basic errors in Judgment relating to the source and the number of shots are possible:

The acoustic stimulus, or shot, has two primary components: the shock wave and muzzle blast (illustrated in Fig. 1); and several echoes, or reflections.


Because a rifle bullet travels at supersonic speed, it generates a shock wave that spreads acoustically in the shape of a cone, with the bullet as the tip of the cone. The muzzle blast, which propagates at the speed of sound, spreads out spherically from the source. Both of these sounds are very loud. The shock Wave has a peak sound pressure level of about 135 dB re 2x10-5N/m2, and the muzzle blast, a peak of 157 dB re 2x10-5N/m(2), at l m. The time between arrivals of these two sounds at a given listener location can vary considerably, depending on the listener's position with respect to the location of the rifle and the path of the bullet. Since the amplitude of the shock wave diminishes as one over the distance from the source and the amplitude of the muzzle blast diminishes as one over the square of the distance from the source, the relative intensity of these two sounds also varies considerably from one listener location to another.

At any reasonable distance, both the conical and spherical waves are essentially plane waves with respect to a small object such as an observer's head. Thus, to determine the apparent locus of the source, we need only take a perpendicular to the appropriate wavefront as it sweeps over the observer. Figure 2 shows the geometry of the two waves at two different times. The shock wave, at time 1, has just reached the observer; its apparent locus is along the path of the bullet on a perpendicular to the shock wave. At this time, the wave from the muzzle blast has not reached the observer. At time 2, when the blast wave has reached the observer, the apparent source of the shot is on a perpendicular to the plane of the spherical blast wave and, therefore, at the muzzle of the rifle.


Dr. George Gariner confirmed this analysis at a test carried out with 20 to 30 observers at the Aberdeen Proving Ground. The observers were seated in rows parallel to the path of the bullet. The blast wave was muffled by firing the rifle through a small hole in an enclosed van. The reports of the observers are portrayed graphically in Fig. 3. About 75% of the observers pointed at the path of the bullet, while 25% pointed away from this path - but still perpendicular to the surface of the conical shock wave.

This latter judgment is called a front-back reversal. If the sound of the shock wave were not so brief, an observer would have time to execute a head motion and tell whether the source was exactly in front of or behind him. However, the shock wave endures for only about 1 msec and the blast wave about 5 msec; some front-back reversals are therefore expected. Even if the muzzle blast is not silenced, the observer may be confused. The further the observer stands away from the muzzle and the nearer the path of the bullet, the more likely that localization of sound will be based on the shock wave and, hence, incorrect.

Some muffling of the blast wave will occur if a rifle is fired from within an open window. Thus, in the acoustical reconstruction, the rifle was fired from two locations in the TSBD: (1) in the plane of the open sixth-floor window and (2) with the muzzle tip withdrawn 2 ft from the plane of the window.

The buildings around the Plaza caused strong reverberations, or echoes, that followed the initial sound by from 0.5 to 1.5 sec. While these reflections caused no confusion to our listeners, who were prepared and expected ot hear them, they may well have


inflated the number of shots reported by the suprised witnesses during the assassination. The source of these echoes can be predicted from the general geometry of the Plaza. For example, one hears a very strong reflection from the Post Office Annex that arrives about 1 sec after the shot, regardless of whether the rifle is fired from the TSBD or the knoll. Because of the long delay, a listener located on the knoll would recognize this as an echo but might place the source somewhere in back of him, anywhere from the TSBD to the railway overpass.

From near the TSBD, a listener would hear a strong echo from the general vicinity of the railway overpass. However, since the initial disturbance, the shock wave from the bullet, would be almost directly overhead -- an anomalous locus, especially if the rifle had been fired from well within the TSBD - this echo would cause some confusion. The general area of the knoll, to the right of the bridge, would then be a prime candidate as the locus of the source. Even though this echo occurs 0.8 sec after the shock wave, it is the first sound that would make sense to the listener. On the other hand, listeners located near the railroad overpass would react to the very strong reflections from along Houston St.

For listeners in the Plaza area, the location of the rifle muzzle relative to the window opening is a critical determiner of the perceived sound. The further inside the building the muzzle is located, the greater the potential for the shock wave to dominate perception. If the muzzle of the rifle had been withdrawn and, therefore, little or no blast were present for one or more of the shots in 1963, the localization judgments of people in the Plaza would have been based primarily on the shock wave, creating much uncertainty and lack of agreement.

During the reconstruction, echoes were heard from the new hotel, but they arrived some seconds after the primary sound and long after the earlier echoes from structures bordering the Plaza. The hotel echoes, therefore, did not interfere with the subjective evaluations in any way.


3.1 Origin of Shots

According to Investigator J. Basteri, 692 people were present in the Plaza during the assassination. Two surveys of interviews and testimony given by some of these people have classified the witness reports as to the origin of gunfire into four categories: the TSBD, the Knoll, Other (not TSBD or Knoll), and Don't Know (origin uncertain). J. Thompson's compilation in Six Seconds in Dallas of 190 witness reports is summarized in Table I.

TSBDKnollOtherDon't KnowTotal

This sample of 190 is 27.4% of the total available witnesses. It is difficult to know what, if any, bias is present in the selection of these witnesses. The sheer size of the sample makes it difficult to believe that a sizable selection bias was present. It is also difficult to predict the effect of a selection bias, if one were present. How could one tell what the witness was likely to report prior to the interview? People were scattered over a large area of the Plaza, but we do not know if equal proportions were selected from each area. This factor could influence the results, since analyses reveal that a person located near the knoll was more likely to report the knoll as the origin of the shots than any other location; similarly, a person located near the TSBD was more likely to report the TSBD as the origin of the shots than any other location.

The House Committee compilation is drawn from witness interviews by the Dallas Police Department and the FBI and from sworn testimony in the Warren Report. The total number of reports in this survey is 178. With very few exceptions, all these people appeared in the 190 sampled by Thompson. Similar sample-selection uncertainties apply here as well. The House Committee analysis is summarized in Table II.


Over half the sample had some opinion as to the origin of the shot; the majority of these reported the origin as the TSBD. Twenty-one witnesses reported the Knoll as the source, 30 reported some Other location, and only 4 witnesses gave more than a single location for the shots. The Four reporting a dual or multiple location are counted as "Other" in Table II. Of the 49 witnesses pointing at TSBD, 13 were at the depository itself, 16 were in the motorcade, and the remainder were scattered throughout the area, including at the Sheriff's Office, the overpass, the knoll, and the triangular park.

A breakdown of these reporting the knoll as the origin of the shots show that 2 of 21 were located on the knoll. Eight were on the curb along Elm St. on the knoll side or on that side of the motorcade traveling down Elm St. Four were near the TSBD. One was on the east side of Houston. Five were in the triangular area bordered by Elm, Houston, and Main, and one was on the railroad overpass.

An analysis of the "Other" responses showed no obvious pattern. Some witnesses at the TSBD point toward Houston St.; others point down Elm. Similarly, those at the Sheriff's Office point in an arc ranging from west of TSBD to the railroad overpass.

Comparing this statistical analysis with Thompson's, the most striking discrepancy is the relatively low percentage of witnesses reporting origins other than the knoll or the TSBD in Thompson's compilation. Another important difference is in the relative number of people pointing at the TSBD is the knoll. Although the categorization of a given response is somewhat arbitrary, the major discrepancy in the two compilations must be laid to a difference in classification of responses making up the compilations. Zapruder is listed in the Thompson survey as pointing to the knoll, while his sworn testimony before the Warren Commission was as follows:*

Liebeler: But you didn't form any opinion at that time as to what direction the shots did come from actually?
Zapruder: No.

Hence, House Committee staff placed his response in the "Don't Know" category.

3.2 Number of Shots

The House Committee compilation also categorized witness responses according to number of shots attributed to the four

*Warren Report, Vol. 7, P. 572.

different categories of origin. This analysis is summarized in Table III.

OriginNo. of Shots
22 or 334Don't KnowTotal
(2.0) (0.8) (15.4) (0.7) (1.1)
(2.9) (1.2) (22) (1.0) (1.5)
Don't Know7261 1 5 76
(7.5) (3.1) (58.6) (2.7) (4.0)

*Expected number of judgments if origin and number of shots were independent judgments.

+Seven other witnesses report 1, 4-5, 5, 6, or 8 shots.

Reports as to the number of shots range from 1 to 8. Of the 178 witnesses, however, the vast majority, 74.2% (132/178), reported 3 shots, and the mean number reported was 2.98.

Given the scatter in the reported sources of the gunfire, one tenable hypothesis is that only people in certain locations might hear the knoll shot. We therefore sought to investigate to what extent the data matrix was interrelated, i.e., to what extent does one Judgment influence the other? One test for this interrelation is to assume the converse --namely, that the Judgments are independent and to determine how well we can predict the entire data matrix on the basis of this hypothesis. The expected number, which is given in parenthesis beneath the number of people actually reporting, is calculated by determining the probability of each report From the margins and assuming that a particular cell, the intersection of that row and column, can be calculated from the product of the probabilities. For example, 20/171 = .117 report the shot coming from the knoll and 132/171 = .772 reported B shots. Thus, the Joint occurrence of both events, assuming they are independent, is (.772) (.117) = .09, and the expected number of such reports is (.09) (171) = 15.4. The number of people reporting shots in this cell of the matrix is 11, 4 or 5 fewer than expected. By and large, the predictions are excellent, and there is no reason to suspect that the two responses are other than independent.


On August 20, 1978, Dr. Dennis McFadden of the Psychology Department of the University of Texas and Dr. Frederick Wightman of the Department of Audlology at Northwestern University listened to the three sequences of shots fired during the acoustical reconstruction and recorded their impressions. Appendix A contains a transcription of their notes. Their reports concerned the apparent origin of shots, any apparent secondary sources or echoes, how loud the shots were, and any other remarks they felt appropriate.

Initially, we were uncertain as to how easy it would be to determine the correct location and what degree of consistency there would be among the observers. Hence, for the first sequence, and during most of the second, the observers were located about 1 m apart and in such a way that I could see and compare their responses. The approximate observer locations each sequence are indicated in Fig. 4. During the first sequence, Dr. Wightman correctly localized all 17 shots, and Dr. McFadden missed only l. Their general qualitative descriptions and descriptions of the reverberations were also highly consistent. We were, therefore, more confident about the consistency of the reports, and during the latter part of the second sequence, Dr. McFadden moved from his original location at the curb at the top of Elm directly in front of the TSBD, to across Elm on the southwest corner of Elm and Houston. For the third sequence, Dr. Wightman and I observed from the grassy triangle formed by Elm, Houston, and Main Sts., while Dr. McFadden observed from the railroad tracks, above the northern curb of Elm.


My own impressions and the reports of Dr. William Hartmann, the investigator of the "Jiggle analysis," were very similar to those of McFadden and Wightman, although my own (hearing )is impaired by about 50 dB in my left ear. The primary manifestation of this difficulty was my failure to hear some echoes if they occurred to my left. Thus, it would seem that our observers, because of their special training and experience, are only slightly more acute concerning nuances of the echoes and reverberations and, perhaps, in separating the shock wave and the blast wave than are untrained people.

The emotional condition of our observers during the test and the emotional condition of the people during the assassination were undoubtedly quite different. The influence of such emotion on the localization Judgment may be quite large, but there is no way to quantify this factor.

4.1Test Conditions

The shot sequence was unknown to both of the observers. Because repeats of certain shots were requested during the sequence, I was also uncertain --despite knowing the planned sequence.

We requested three motorcycles to be running during the test to provide some background noise that would approximate the original listening conditions in Dealey Plaza. Unfortunately, these newer motorcycles were not very noisy, but the shots were so loud that any reasonable level of background noise would have been low in comparison with the shots themselves. Our listening conditions were, therefore, essentially representative of those at the time of the assassination, except for our being able to hear some very-low-level, long-delay echoes that originally might have been inaudible.

Our observers did know that there were only two possible locations for the marksman, whereas there was considerably more uncertainty on this issue at the time of the assassination. Signal uncertainty of this kind generally does not seriously degrade the accuracy of Judgments, but it does depend on the number of potential alternatives. In this case, as we shall see, the localization reports made by the trained listeners were, for the most part, of general areas, rather than specific windows of a building. The total number of potential locations was not, therefore, large and, thus, was likely to be representative of localization responses given at the time of the assassination.

4.2 Analysis of Observers' Localization Responses

The descriptive comments made by the observers are difficult to compare with any degree of precision. However, there was clear agreement in their reports with respect to the apparent loudness of the sounds and echoes and the apparent size of the acoustic image. After each test shot, we asked the two observers to guess whether the shot was fired from the TSBD or the knoll, independent of what the apparent locus might be.

Table IV is an analysis of this forced-choice data.

SequenceDr. WightmanDr. McFadden
112/12 100%11/12 92%
211/15 73%14/15 93%
319/25 76%23/25 92%
Overall47/57 82%53/57 93%

Overall Agreement 82%

The average accuracy of the reports is nearly 90%, and the consistency between the two observers is 82%. Also, the average accuracy is nearly exactly the same whether the shot came from the TSBD or the knoll. Thus, this analysis shows high accuracy in localizing the source of the sound and reasonably good consistency.

4.3 Loudness and Apparent Size of Acoustic Image

All observers rated the rifle shots as very very loud, and they were unable to understand how they could have been described as a firecracker or backfire. Only the pistol, which was subsonic, produced a moderate loudness.

Practically all the rifle shots, whether fired from the knoll or the TSBD, appeared to be diffuse and to occupy a very large acoustic space. For example, the sound did not seem to come from the sixth floor window of the TSBD, but from the right upper side of the building. This apparently large source location may be a result of acoustic scatter of the muzzle blast -either because of the building in the case of the TSBD or because of the trees in the case of the knoll. Only the pistol shot appears to have a reasonably constrained acoustic image and, for that reason, could be localized with some precision.

One might consider whether silencers would change the apparent loudness of the size of the image. The Garinther-Moreland study* reports the average attenuation produced by a number of silencers as being about 18 dB for all weapon-silencer combinations. Sound from the supersonic weapons tested were attenuated

*"Acoustical Considerations for a Silent Weapon System: A Feasibility Study," 1966, p. 70.

by 18.6 dB and 37.5 dB, but even with this reduction, the peak overpressure was still very large. Two rifle-silencer combinations produced peak overpressures of 138 dB and 120 dB at 3.8 m, clearly loud enough to be easy to locate and clearly audible above the motorcycle and crowd noise.


It is difficult to draw any firm conclusions relating the reports of witnesses in the Plaza to the possible locus of any assassin. Confusion between the shock wave and muzzle blast front-back reversals, confusion caused by echoes, and the startle of the witness could all be used to impeach the testimony of any particular witness. There is no way of knowing which, if any, of these factors was most significant with respect to any single observation made on November 22, 1963. Thus, one witness can be assigned no more credibility than any other. For example, even if a shot was fired from the TSBD, the witnesses standing on the knoll would likely report the source of the shot in the following way. The witness would presumably localize on the basis Of the shock wave. With the path of the bullet behind the President's car, the witness would perceive the apparent locus of the shot as being on a line from himself to the bullet's path -- i.e., in the street or open park behind the path of the bullet. ,Since this location is impossible, a front-back reversal is likely. This front-back reversal would place the source 180(deg). behind the bullet path and, hence, on the knoll.

Despite this uncertainty, two general remarks seem worthwhile--one based on the test, the other on the statistical analysis.

First, it is hard to believe a rifle was fired from the knoll. Such a shot would be extremely loud, even if silenced, and it would be hard to imagine anyone in the vicinity of the knoll missing such an event. An unsilenced pistol firing subsonic bullets also seems unlikely because this shot was the easiest to localize of all the shots fired. It produced the least reverberation. As an acoustic image, it was much sharper and less diffuse than that of the rifle, sounding much like a firecracker. It is, however, conceivable that had a pistol been fired from the knoll at about the same time a rifle was fired from the TSBD the pistol shot would have been less easily localized, or even completely masked from some vantage points. As an isolated shot, however, it is extremely easy to localize.

Finally, if one accepts the hypothesis that a marksman fired from the knoll and that other shots were fired from some other location, then it seems most unlikely that only 4 of 178 witnesses would report a single location as the origin of the shots. Despite the various causes of confusion in the locus of any single shot, a second shot from a different location should be distinctive and different enough to cause more than four witnesses to report multiple origins for the shots.


The tabular information in this appendix was transcribed from notes made during the acoustical reconstruction on August 20, 1978 by two trained observers --Dennis McFadden and Frederick Wightman. Included in this table, along with their responses, are the number of the shot in each sequence of test firing, the origin of the shot, and the target fired upon. For convenience in determining the positions of rifle, target, and listener, the reader may refer to Fig. 4 of this report.

Abbreviations used within the table are as follows:

* T always refers to the TSBD and K to the knoll.

*In the column headed origin, Tp means the rifle was fired in the plane of the sixth floor window of the TSBD, T2 means the muzzle was withdrawn 2 ft from the plane of the window, K indicates a rifle shot from the knoll, and Kp represents a pistol shot from the knoll.