Today I am taking a break from acoustics, and working on my MBA assignments.
Except I’m not. Like most everyone else on the Internet I am keeping one eye on the trial of Oscar Pistorius. And today there have been a couple of acoustic issues raised which have piqued my interest.
I’m hoping that an acoustic expert will be introduced to the trial to answer these questions properly, but in the meantime (or in case it never happens) I hope you will find this interesting. So much of the evidence in the first two days is based on “who heard what” that it would seem a major oversight for it not to be examined properly.
A caveat: I’ve done this as a desktop assessment, in an afternoon. I’ve had to make assumptions (which I hope are clear), I don’t know the site, and I don’t know things like the building materials, where the windows are, etc. In a forensic acoustics project the standard of investigation and assessment would be significantly more accurate, as you would expect.
I also don’t have any opinion on the case, and would stress to all of my readers that there will be more to decide on legally than just the acoustic evidence. What I present here is intended to demonstrate how acoustics can be used, and hopefully make more people interested in how sound “works”.
I was asked on Twitter today about claims that Reeva Steenkamp could not have screamed as she would have been too seriously injured by gunshots. Michelle Burger testified that “I heard shots and I heard screams…I still heard screaming once the shots started”
My Twitter correspondent asked if it was in any way possible that the sound of gunshots could travel faster than the sound of a scream, so that they would be heard in the opposite order from which they happened.
The simple answer to that one is no. The speed of sound varies according to the medium (air, water etc), and according to temperature. But two noise sources occurring in the same conditions, at the same location, and heard at the same receiver point, would be heard in the order in which they occurred.
Alright, so, who was screaming? Could you tell the difference between a woman screaming, and a man crying or wailing?
To my mind, that will come down to the frequency content of the sound.
The spectrograms presented by Prof Dan Fleetwood show differences between male and female screams.
You can see that these have quite different characteristics, so I believe that you could tell whether it was a man or a woman screaming, even at some distance.
However, what I’m not sure about is whether a male keening / crying sound would be as distinct. I’d expect it to encompass more frequencies, but temporally it would also be different from the short burst of a scream.
So I’m undecided on this one, but unless I can persuade my husband to cry for me when I’ve got the sound level meter out, we’ll have to settle for “yes you probably could tell the difference”.
There’s no doubt shots were fired, and no reason to doubt that a cricket bat was used to smash the door down. Again, though, this made me wonder if you could tell the difference.
In this Acoustical Society of America paper A variety of guns are estimated at a sound pressure level of 152-160 dBA at a distance of 1m.
My gut reaction is that however loudly you battered a door, you wouldn’t be able to get close to this – the best I was able to manage in a very unscientific experiment was 95 dBA at 1m.
Subjectively, an increase in sound pressure level of 10 dBA is interpreted by humans as an approximate doubling of loudness. On this basis a gunshot would be many times louder than even a very strong, adrenaline fuelled male human.
Based on that alone, it seems that a gunshot would be noticeably louder than hammering on a door. But perhaps the door could sound like a gunshot, only much further away? After all, both would be impulsive (sudden) sounds. Is there a difference in the frequency spectrum which would differentiate them?
Well, a gunshot has most of its energy concentrated around 750 Hz – 3kHz and above.
By contrast, a door being hit with a wooden bat is, essentially, a really loud door knock. Because the door has an air cavity behind it (the room), and a typical domestic door is relatively lightweight, you’d expect quite a bassy sound, as well as the higher frequency content of the impact itself.
In the interests of science, and unable to locate a sound for “door being hit with bat” on the internet, I whacked our bathroom door with a broom handle. That was a bit too rattly so I tried to simulate something more robust using wooden floorboards over a cellar, which you can hear here.
Not entirely scientific, but sounds quite different to a 9mm gunshot. And a different spectral shape too.
(axes are dB Lmax in the vertical, and third octave band centre frequency in the horizontal)
Based on this, I don’t think you could mistake a door being broken down for a gunshot.
Although it’s at the end of this blog, this was the biggest question for me. We have been told that the Burger house is 177m away from the scene and that their windows were open with no AC noise. We’ve been told that Reeva Steenkamp was in an enclosed bathroom, with the door and window closed.
What I don’t know is whether the Burger balcony directly faces the bathroom window, whether there is a direct line of sight between the two houses, or whether there are buildings in between, and the background noise level on a Pretoria housing estate at 3am. I also don’t know what the windows and wall are made of, how big they are etc. All of this would be important in carrying out this calculation properly. So there are assumptions made in what follows.
I found a super paper on “The Forensic Analysis of the Audibility of Female Screams” by Durand Begault who measured a “typical” very loud scream at 1m at 114 dBA.
For the sake of simplicity remaining in single figures (it would be better to analyse across the frequency spectrum), even from a small reverberant room with a fairly poor window, I would expect this to be reduced to about 80 dB just outside the building.
Over a distance of 177m, using point source attenuation, this would be reduced by a further 45 dBA, giving us 35 dBA outside the Burgers’ house. Now allow for around 15 dBA attenuation through an open window for a level of 20 dBA in their bedroom (note; I’m assuming they heard the screams from their bed not from the balcony).
The audibility of any particular sound is going to be affected by the background noise that it is heard against – the signal to noise ratio. If the scream is at a similar level to, or below the background, it would be very difficult to hear. As I say, I’m not familiar with Pretoria at all, but in the UK a quiet night in a residential area might get down to 30 dBA. In my fairly rural bedroom it’s about 25 dBA with the windows open.
Therefore even assuming that it was otherwise very quiet, the screams would be around 5 dBA lower than the background noise level when heard inside the house, or 5 dBA higher when heard outside. So if everything is as I have assumed in my conservative scenario, you may possibly just have heard screams from outside.
But this is where the unknowns come into play – as described above there are other factors which would affect the level of noise transmitted from the scene to the balcony / house – in particular the effect of shielding from intervening buildings, as well as angle of view if the window and balcony do not directly face each other. A higher background noise level would also reduce the sound transmitted.
What does this prove? Well, nothing much, other than that my gut reaction that hearing “the scream” over that distance is unlikely, particularly from inside a bedroom. Hopefully, however, I have also demonstrated in a fairly lightweight way the ways in which acoustics can be used to solve problems and answer questions.
Acousticians often appear as expert witnesses, particularly in planning hearings, but occasionally in criminal cases too. Let’s hope that some rigorous scientific evidence from acousticians will be presented in the Pistorius case, and that the outcome won’t be decided on the basis of “who says they heard what”.
(note: there is a follow up article, which you can read here)