Theoretical analysis of acoustics of Stonehenge from archaeological plans
This project was to be focused principally on phase IIIc of Stonehenge’s stone circle, with the hope of future work on other phases. Using archaeological drawings of Stonehenge, a basic acoustic analysis of the site was carried out. This was done by considering reflections of sound from various sources, calculating delay times of principal reflections, assessing likely reverberation and likely positions and modes of standing waves. It was immediately apparent that the Sarsen stone circle, and in particular the circle of stone lintels of the Sarsen circle, would be a highly significant acoustic feature. Standing just inside the circle would be acoustically significant, as edge effects by the wall would boost low frequencies.
A basic study was carried out, tracing ray paths for the transmission of sound in the space and considering materials, surfaces and reflections. It was clear that sound would move most freely between the outer Sarsen and the bluestone circle. It seemed possible from this, that there might have been some sort of partial whispering gallery effect. The lack of a continuous wall, the spaces between stones, may have created a series of echoes, rather than the whispering gallery effect caused by the coherent transmission of sound around a curving stone wall, such as that found at St. Paul’s Cathedral in London, or the Baptistry at Pisa. These and other circular stone sites of ritual significance were investigated for comparison, and several were found to have well known acoustic effects. A circular stone building will be likely in most cases to have some acoustic effects.
Figure 1 shows how a sound made at the edge of the circle would have reflected off each fifth (red dotted line), fourth (blue) and third (green) stone as it moved around the circle. Each reflection would change the quality of the sound, and also delay its travel, causing sound to arrive later than sound travelling directly. The sound travelling from the bottom of figure 1 to the top of the picture, around the walls of the circle, would arrive later than that travelling straight upwards. This is likely to result in reverberation, or perhaps a series of discrete delays or echoes sounding somewhat like a galloping horse. It could otherwise produce a chorusing effect, depending on how long the time delays were. Figure 1 also shows how the altar stone in the centre of the space may have acted to project the sound (yellow line) of someone in the centre towards the entrance of the space and down towards the avenue, the ceremonial approach to the circle beyond its bounds.
Similar calculations illustrated that the centre would act as a particular acoustic focus, reflecting sound back from all directions. Moving to the exact centre of the space would result in the sudden activation of the acoustic, giving a radically different result to that experienced only perhaps a metre away. From this central position, the trilithons seemed to be shaped as much like a megaphone as a horseshoe, focusing and projecting sound towards the avenue. The bluestone horseshoe seemed to have a similar effect. There was a clear acoustic orientation, a ‘front’ and a ‘back’. The entrance from the avenue was a clear acoustic focus (front), where there were more sonic effects. The Heel stone, slaughter stone and portal stones, some of which were in line with the avenue and entrance to the stone circle, would be likely to produce interesting echo effects, and to reinforce acoustic effects such as resonance.
Figure 1: Theoretical Consideration of Sound Reflections in Stonehenge.
It was clear from the shape of the space and materials used, that there would be likely to be acoustic resonance, echo and reverberation. Because of the large size of the space, the resonances and standing waves might produce a low humming and/or echoes. One could perhaps have stimulated these resonant frequencies of the space either by playing rhythmic music, or by working in a manner that made a noise, such as working stone rhythmically to shape it, especially if one played in time to the echoes in the space. I theorised that there would be strong echoes in the space, using basic calculations based on the speed of sound and distances such as the diameter of the stone circle and distance to the heel stone. For example, sound would leave a percussive noise made on one side of the stone circle, bounce off the opposite wall, and return later as an echo. Knowing the speed of sound, and the distance taken, we can calculate the time taken, the delay time, and its associated frequency.
Speed of sound V = 344m/s = distance / time
Distance from one side of the stone circle to the other and back = 33m x 2
Time delay = 66 / 343 = 0.19s, frequency of echo at Heel = 5.2Hz
5.2Hz is equivalent a rhythm at 156bpm (quavers).
Frequency at Centre = 10.4 Hz, equivalent to 156bpm (semiquavers) or 0.1s
I encountered no mentions of such echoes in the existing literature. Thus it seems that at the edge of the stone circle there may have been echoes at a slower (and easier to hear and play along to), tempo than in the centre. At the central position, the echo may have doubled in speed.
Such echoes can also appear as resonance in the space, either at this very low frequency, or at octave multiples or frequency doublings. The kind of resonance that could be developed in the space, might be the equivalent of playing a very slow roll on a kettle drum, or another large drum, to make it ring. Another analogy is the flute like sound that can be made by blowing over the top of a bottle. In each case the movement of air is constrained and controlled, by the drum skin and body, or the glass of the bottle, and air is stimulated into movement by hitting the skin or blowing across the bottle top. At Stonehenge, the sarsen stone and bluestone circles and their lintel rings would constrain the air, which could be stimulated by human sound, or even perhaps by the wind. As Hardy had suggested, there might indeed be a low hum or booming sound, caused by the primary circular or cylindrical resonance of the space.
These kinds of frequency, below 20Hz, are sometimes called ‘infrasound’, and often described as being below the range of human hearing. However, this is a little misleading.
Sound remains audible at frequencies well below 16 Hz. The limit of 16 Hz, or more commonly considered as 20 Hz, arises from the lower frequency limit for which the standardized equal loudness hearing contours have been measured, not from the lower limit of hearing.
It would be heard by human ears if it were at a high enough volume. Sound is not inaudible below 20Hz, but has to be increasingly loud for us to hear it, at 10.4Hz 97dB and at 5.2Hz as much as 106dB. Older people can hear these low frequencies more easily, just as the young can hear higher frequencies. Loud percussion noises could these levels. Such low frequencies are often heard in the form of a rhythmic echo, rather than a sustained pitch or note. If one clapped one’s hands, a 10.4Hz echo would provide an effect a little like a simple tapping rhythm with a tempo of about 156 bpm, hearing a semi-quaver pulse.
The spaces between the lintels and uprights of the sarsen stone circle and trilithons (and perhaps the blue stone circle if it had lintels), could be significant resonant spaces and produce unusual resonant effects. The outer bank would be significant in that it would contain the sound within the space. The floor material would be important. Whether it was chalk, mud or grass could make a significant difference. Acoustic effects would be likely to be most pronounced at the centre. There would also be echoes as sounds made returned to the centre of the space, bounced off the stones outside the circle (Heel Stone, Slaughter Stone, Station Stones), or reflected around the circle. It appeared that the main echo would have a delay time of around 0.2s, a frequency of around 5.2Hz. This might be heard at 10.4Hz (0.1s), depending on where the sound reflected, and related low frequencies may be heard.
Watson’s results had indicated that sound would be contained within the stone circle, creating a sense of envelopment within the space and a change in sound when entering. Theoretical analysis had indicated the presence of resonance, a low hum possibly, echoes, reverberation, particular effects at the centre. The next stage of the process was to use a model to in order to explore further.
 The earliest stones present, and the principal other type of stone at the site, are often referred to as Bluestones. These are made from Spotted Dolorite from Preseli in Wales. Recent work by Paul Devereux has shown that a village in the area was called Maenclochog (Ringing Stones), and that it was known that stone in the area had particular acoustic effects. Paul Devereux and Jon Wozencroft, ‘A Stone Age Holy Land?’, http://www.landscape-perception.com, (27th March 2009).
 This effect allows the whispered speech of someone standing distance from a second person to be heard clearly, even though the distance would normally mean nothing could be heard. This effect is often observed when standing at different points of continuous circular stone walls.
 The trilithons each consist of three stones, a large pairs of upright stones with a stone lintel joining them at the top. They are the tallest stones in the space.
 156bpm stands for 156 Beats Per Minute, this is usually written in classical music scores as crotchet equals 156.
 Geoff Leventhall, ‘What is infrasound?’, Progress in Biophysics and Molecular Biology, 93, (2007) pp. 130–137.
 Aaron Watson, 2006.