The present work provides a small sonic analysis of gravitational wave GW150914 produced by the merger of two black holes. When the black holes merged, they produced a significant gravitational wave that was detected by the LIGO lab. I will begin by explaining the nature of space’s vacuum, how black holes are going to be conceptually understood, and finally what gravitational waves are. This will be followed by the interpretation of the audio provided by LIGO using Audacity as the tool for analysis.

Introduction

Space is commonly understood to be a vacuum devoid of air and accordingly, of sound. This isn’t strictly the case. Properly understood, space is a vacuum, but it isn’t empty. On Earth, a cubic centimetre of air has ~ 10¹⁹ atoms whereas gas close to the Sun has 1 atom per cubic centimetre, which means space has quite a powerful vacuum but it is not devoid of material in between the bodies which occupy it (Binney 2016, 11). Since sound is produced by the fluctuations in the density of atoms of air, space is woefully inadequate medium for sound transfer. Human hearing ranges from 20 Hz to approximately 20 000 Hz—and given the above, this means any sound produced in space will transmit at a frequency too low for human hearing to register (Purves et al. 2001).

For the purposes of this work, a black hole will be considered as follows: a highly curved region of spacetime that result from the accumulation of substantial amounts of matter; the resultant curvature is so large there is a region of no escape. Black holes are some of the most potent and complex objects in the universe. The ways in which they work are generally mysterious and are still the subject of intense debate; lately this has surrounded the concept of the singularity[1]. Still, for the purposes of this work, these complexities will be largely ignored, except insofar as they are important when discussing the merger observed by LIGO. This is not to say that they are not worth studying, simply that the scope of the complexities of black holes are beyond the scope of this paper.

A final introductory remark concerns the nature of gravitational waves. These were detected directly for the first time on 14 September 2015, the particular wave is known as GW150914; incidentally this is the focus of this brief. Gravitational waves are best described as distortions of spacetime that “propagate through the Universe at the speed of light” which are caused by “concentrations of mass (or energy) which warp space-time” experiencing “changes in...shape or position” (Barish 1999, 1). These waves bear some similarity to sound waves in that they both persist through mediums, however their mediums are rather distinct (i.e., sound waves vibrate through air, water, and so on while gravitational waves cause ripples in spacetime). One of the most critical similarities is that they can both be detected and catalogued accurately, and hence LIGO gained insight into the merger of two black holes, each at 30M_☉ which occurred at a redshift of approximately 0.09 (Maggiore 2018, 285; Abbott et al. 2016b, 2).

Merger Properties

The orbit frequencies began at $f\simeq 30Hz$ and peaked at $f\simeq 144Hz$ (Maggiore 2018, 285). This means the black holes orbited each other, at their moment of joining, at about 72 Hz and because of this high rate, generated a significant output of energy (285). This energy emerged in the form of a gravitational wave that LIGO captured and measured. The video and audio of its sound, however, is based on a conversion of the gravitational wave and its relevant parameters into something audibly intelligible to humans. When the merger’s basic sound conversion from LIGO is performed in Audacity by using the sound file from the video released by LIGO, several interesting things are observed. First, the sound of the first peak of the wave 54 Hz with other peaks existing at 86 Hz, 102 Hz, 122 Hz, and 144 Hz. These seem to be the most obvious tones in the sound, but higher peaks exist as the graph evidences.

Figure 1: A frequency analysis of GW150914 using Audacity.

With respect to fig. 1, one observes that the chirp initially peaks in frequency at the lower range and tapers off as it passes 400 Hz. Indeed, the ‘chirp’ researchers encountered was low in frequency and is sonically more akin to a ‘thump’. The density of low frequencies being greater in intensity than higher frequencies contributes to this ‘thumping’ sonic quality. This analysis in Audacity can be detailed further when the chirp is plotted on a spectral and waveform basis. I provide illustrations of these below.

Figure 2: An analysis of GW150914 in Audacity showing waveform and spectral information.

This is a focused view of the ‘chirp’ itself in both waveform below and spectral view above. When examining the spectral graph, it is clear that it matches quite well with the frequency analysis, but also shows that a lot of the generated ‘sound’ is low in register. There are traces of sound at higher frequencies, but these are rather faint and do not impact the sound profile substantially. Below the spectral graph, the waveform graph represents the range of amplitude detected in the sonic profile of GW150914. What is particularly interesting is how this graph shows the sudden falloff of the sound; the chirp is abrupt and its relative period short and quickly it fades into the background noise. The substantive part of the sound’s profile as seen in the waveform is noticeably dense at lower frequencies in the spectral view; this is can be gleaned from fig. 1 as well.

Figure 3: A zoomed-in view of the multi view analysis of GW150914 using Audacity.

This zoomed-in view of the spectral and waveform graphs reveal more detail about the trace amounts and relative densities of frequencies present in the sound. There are clearly oscillations of a much lower frequency at the start of the chirp (approx. 0.700s) and a gradual shift to oscillations at higher frequency (approx 0.725s). The oscillations' uniqueness emerges properly around 0.700s and tapers by about 0.750s. Note the trace amounts of high frequencies. The full range of the spectral graph can be better examined in the detailed image below.

Figure 4: A detailed spectral view of GW150914 using Audacity.

Though it appears there are lines that extend to roughly 10 000 Hz (at approx. 0.730s), these are very low in relative density and as such impact the sound to a much lesser degree. The bands near 300 Hz and 600 Hz are much more impactful to the human listener as their density is significantly greater, as the colour of that region of the graph permits us to observe.

Conclusions

From the above background and data, it is clear that GW150914 presents a unique sonic profile that is low in frequency, very quick—its most noticeable profile lasts for about 0.07 seconds—and an audible rendition of a very powerful cosmic event. Much of the work that underlies the nature of the gravitational wave’s frequency (i.e., distinct from its sonic conversion) is beyond the scope of this work but can be found in the original works published by Abbott et al. (2016a, 2016b) as well as in other resources like Maggiore (2018). What can be definitely said is that this sonic representation of a gravitational wave captures and to an extent—demystifies—a great cosmic event that has taken a long time to reach the Earth. Indeed, this exploration reveals that space is not, at least not with a bit of measurement and conversion, devoid of sound.

Bibliography

Abbott, B. P., R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, K. Ackley, C. Adams, et al. 2016a. "Observation of Gravitational Waves from a Binary Black Hole Merger." Physical Review Letters 116 (6): 061102-061102.

Abbott, B. P., R. Abbott, T. D. Abbott, M. R. Abernathy, F. Acernese, K. Ackley, C. Adams, et al. 2016b. "Properties of the Binary Black Hole Merger GW150914." Physical Review Letters 116 (24): 241102-241102.

Barish, Barry C. 1999. "The Detection of Gravitational Waves with LIGO."

Binney, James and Oxford Very Short Introductions. 2016. Astrophysics: A Very Short Introduction. First ed. Vol. 470. Oxford, United Kingdom: Oxford University Press.

Blundell, Katherine M. and Oxford Very Short Introductions. 2015. Black Holes: A Very Short Introduction. First ed. Vol. 453. Oxford, United Kingdom: Oxford University Press.

Kerr, R. P. 2023. Do Black Holes have Singularities?. Ithaca: Cornell University Library, arXiv.org. doi:10.48550/arxiv.2312.00841.

Maggiore, Michele, 'GWs from compact binaries. Observations', Gravitational Waves: Volume 2: Astrophysics and Cosmology (Oxford, 2018; online edn, Oxford Academic, 24 May 2018), https://doi.org/10.1093/oso/9780198570899.003.0006

Purves D., G.J. Augustine, D. Fitzpatrick, et al., editors. 2001. Neuroscience. 2nd edition. Sunderland (MA): Sinauer Associates; 2001. The Audible Spectrum. Available from: https://www.ncbi.nlm.nih.gov/books/NBK10924/

[1] See Kerr (2023) “Do Black Holes have Singularities?”