Tag Archives: sound waves

Who is ignorant of motion is ignorant of nature

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The major contributions to science that Galileo brought to the world are well known. But putting these discoveries in the musical context could turn out to be more relevant that one would think.

The origin of Western science is linked to the study of harmony. As it was understood, Harmonia comes to be in all respect out of contraries; for Harmonia is the unity of multiplicity, and the agreement of things that disagree (the fitting together of extremes).

The Pythagorean school of philosophy sought to integrate scientific inquiry into the nature of Number and a mythical awareness of the musicality of universal law. In particular, the harmonic series consisted of whole numbers: 2/1, 3/2, 4/3, 5/4…and so on.

The instrument that was used to investigate numbers was the monochord (see my previous blog post on the subject), which is used to measure the relationship or ratios between harmonics of a root note (the fundamental).

In fact, some historians of science contend that the division of the monochord strings is possibly one of the earliest scientific-empirical experiments ever to be carried out with mathematical rigor.

Image of a monochord played by a monk

Throughout the whole of history, right up to the eighteenth century, the monochord was associated with cosmic concerns…the stretched string stood for the universe, with the various harmonics representing the planets in the solar system. Music, mathematics, and astronomy were inexorably linked in the monochord. The universe was thought to obey musical laws; therefore, the study of the monochord yielded information considered relevant to the other sciences, the humanities, and religion. Keeping with this harmonic-based cosmology, Kepler discovered a numerical relationship, his third law of planetary motion where the major semi-axis of the orbits of planets and their periods are proportionately related. He called it the “Harmonic Law”, and like all the philosophers of the time, he studied the ancient world of Pythagorus and Plato (Kepler also attempted to fit all the orbits of the 6 planets in nested Platonic solids).

Ancient cultures, before the invention of the printing press and the proliferation of books, were far more sonically oriented than visually focussed. That made them more receptive of the subtleties of the nature of pure tones.

Galileo was born into a musical family, and his father Vincenzio, beside being an excellent lutenist, was also a music theorist, and was investigating tuning. There was at the time a controversy about which form of tuning was best: on one side was the ‘natural’ tuning based on the harmonics of the monochord, and on the other side a more “tempered” tuning, which sounded more pleasing to the ears, in particular the major third- which sounded a bit harsh in the ’natural’ tuning. Also, the pure tuning limited the number of keys the instruments could play in. Galileo, who also played the lute, helped his father in his research. This research involved weighted strings which were set up similar to monochords.

There are several examples of how Galileo would have used music in his research:

In order to keep time while conducting his studies of the motion of bodies and their rate of fall, he used a ball rolling on an incline, by spacing frets at increasing distances from one another in order to hear a steady beat. If the frets were spaced evenly the ball would hit them at an increasing rate. At the time there was no clock precise enough to measure this. The obvious solution was music. Sing a song and the beat will be steady. This was first suggested in 1973 by Stillman Drake, a leading Galileo expert. 

After Galileo discovered the moons of Jupiter, he spent a long time figuring out their periods, in an unsuccessful attempt to use their orbits as a clock to help navigators establish their position at sea, since the first three moons- Io, Europa and Ganymede, were locked in a harmonic ratio of 4:2:1 at one octave from each other.

I think it makes sense to mention that during the experiment at the Tower of Pisa (if it ever happened), the sound of the two objects hitting the hard surface of the ground would have been much more accurately measured by the sound made than by looking at them. The rate at which our ears can distinguish singular events from one another is four times more precise as the one our eyes can.

So thinking about Galileo and the work he did assisting his father with tuning, I am sure his inquisitive mind must have stretched the boundaries of these investigations, and I dare to come up with the following insight:

Coming back to the experiment at the Tower of Pisa, I started to wonder if there was not some connection with the “weighted string experiment” which is how some monochords are set up: by hanging weights at the end of strings. And trying to understand what would be the common phenomena of the falling object and the production of the tones on the strings put into tension by the weights. It dawned on me that there could be a direct connection:

  • the weight (let us say they are stones), initially are at rest, and have potential energy, each linked to their mass
  • this energy is unlocked when put in motion, either when released from the top of the tower or from being hung from the strings they are attached to. None of the phenomenon in these configurations – the falling of the stones or the tones emitted by the strings in tension from the weights – are possible without gravity.
  • as the weight of the stones’ sizes differ, the tension on the string varies.
  • in order to reveal their tension, we have to pluck them, which gives them energy (the same goes for the stones- we have to nudge them over the tower’s edge to use gravity to put them in motion)
  • as it is apparent in the stones’ varying sizes, each string produces a tone that is proportional to the size (in that case inversely proportional, the smaller stone giving the lowest tone) of the stone
  • the energy given to the string manifested in its tension is equivalent to the energy produced by the gravity acting on the stone, both directly related to their potential.
  • you could assume that if you pluck two strings together, they should not reach our ears at the same time, as the lower frequency (being of a lower energy tied to the lighter stone) would take longer to travel in the air than the one with the higher frequency (tied to the heavier stone) as you would assume that the lighter weight would fall at a slower rate. But they don’t, they reach our ears at the exact same time (we never question this because it is so obvious). 
  • but both phenomena, the plucking and the falling, are merely a translation (or to use a musical term, a transposition) of the same initial fact: the size of the stones, and both are a form of motion. The only difference is that one (the sound waves) do not have friction (actually traveling through the medium of the air). So if we remove the friction on the stones, you should end up with the same result and they would hit the ground at the same time, as demonstrated by cosmonaut David Scott of Apollo XV on the Moon – as the different notes reach our ears at the same time.

So it could have been that this correlation was revealed to Galileo during the experimentations he performed with his father, and the root of these physics could very well be music. it seems to me that we have the same initial state give rise to a similar effect, demonstrated by two phenomena, connected through the bridge of the Monochord acting as a phase transition acting on the energy of the stone. 

The various stones fall at the same rate and the various sound waves travel at the same rate.

Of course these are conjectures; it might not be the way his train of thought worked out. But I think there is a chance, and it is an interesting proposition, and it shows that the Law of moving bodies can be deduced with this old instrument, the monochord.

To close, it is interesting to know that in the past ten years the relationship between science and music has been revived and has revealed to us elements in our data set that would not be so easy to discern if the information was offered to us visually only. There are many examples – from exoplanet systems, asteroseismology, gravity waves, and so on. (View my previous posts)

When you listen to the music of Galileo’s time, it is important to try to imagine what was the acoustic environment in which it was conceived and performed. It clearly illustrates the unique position he held in the history of human knowledge with one foot in the ancient world and the other in the modern world. He was, to use a trendy word, an inflection point not possible without the past but enabling the future.

Can we hear all sound waves?

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The obvious answer is no, because some waves are at frequencies our ears cannot detect (about 30 Hz on the low end and 18 kHz on the high end, although most of us have a hard time hearing beyond 12 kHz). But this is only a very anthropocentric view. Many other species can hear way beyond the human range, the most well known being elephants on the low end and bats on the high end, and we don’t really know the full extent of the animal kingdom’s ability to hear the full range of sound frequencies.

But this blog is about the full range of sound waves we can detect, even the ones no living creature can hear. To achieve this, I need to make a very general and fundamental definition for this phenomena. Sound waves are, in their most basic definition, a form of energy transmission. There must be some kind of impulse before a sound wave is produced, as every musician knows – looking at your instrument will not produce a sound, no matter how much you concentrate on it. Strings need to be plucked, drums to be struck, and wind must be blown in your trumpet in order to produce a sound wave. In other words, energy has to be spent for the sound to be emitted and the wave to spread to your ears.

So- waves are energy in motion. But it is important to remember that there are two kinds of waves: sound waves and electromagnetic waves. The fundamental difference between the two is that the first needs a medium to travel in, and the second doesn’t. Both are waves, which makes them energy in motion. Electromagnetic waves create their own magnetic field, which allow them to travel through empty space. Sound waves have many mediums available for their transmission: air is the first that comes to mind. But let’s not forget that this applies to all of the gases, (interestingly, the latest NASA Mars rover “Perseverance” carries a couple of microphones and the recordings tell us a lot about the Mars atmosphere, its composition and pressure, and how the sound propagates), but solids also transmit sound at different rates depending on their density (the only way we know about the inside of the Earth is through sound waves). And not to forget the other medium of water, in which sound waves travel longer and faster than in the air.

Let’s not stop here! Stars have sound waves traveling through them; in fact, they ring like bells, and even minutes after the Big Bang, sound waves bounced around the plasma of particle soup that predates the formation of matter and may have been the kernels of density that allowed the stars and galaxies we see today across the universe to form.

Now we have reached the astronomy scale – the size in which the newest form of waves were first detected in 2016 (although these waves were predicted 100 years earlier, thanks to the theory of relativity). These are called Gravity Waves, and they are an interesting bunch, because the medium they travel in is literally the fabric of space-time, and there again are two kinds, the high frequency ones and the low frequency ones. Their range goes from the millisecond to years. They are created by the most energetic phenomenas in the universe: black holes and neutron stars. The shorter gravity waves come from the merger of these objects; and the longer waves by their orbits around each other.

We cannot “feel” them. These waves are extremely faint, but new instruments like LIGO in the United States, Virgo in Europe, and KAGRA in Japan are detecting them almost daily. There is an application that lets you know when one is detected. You do not feel them but the atoms in your body do, so you can shudder and be a bit thrilled to be a part of the universe in this way.

These gravitational waves are somewhat in between sound waves and electromagnetic waves, both traveling through empty space, but they tend to be closer to sound waves because they do need a medium to go through- although this one is the fabric of space, the same fabric that makes planets circle around stars.

To conclude, I would say that as I dig deeper in the wave phenomena, my title for this blog post has to be answered in the negative. In the process of answering the question, ‘can we hear all sound waves?’, I discovered that there are more sound waves than meet the ears. But we can transpose them and raise their amplitude, and partake in the symphony of the cosmos.

Here is the link to the gravitational-wave-events app:

https://apps.apple.com/us/app/gravitational-wave-events/id1441897107

The Power of Sound

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Most of us understand that sound needs a medium to transmit itself, but not, at least in my case, that this includes any form of matter that constitutes our Baryonic universe. It turns out that this has monumental implications in how fundamental sound waves are in the universe we live in.

When I am talking about a ‘medium’, this applies to all matter in its many forms:

– gases, the most common of which make up our atmosphere in which sound travel at 1,235 meters per second;

– liquids, water from which we are made mostly, in which, due to its higher density, carries sound waves at 1497 m/s;

– solids of course of still higher density, for steel the most dense of solid, the speed is 5930 m/s. Another less well known form of matter is:

– plasma found in extreme invironment like stars or the early universe, but nevertheless does conduct sound waves, like other states of matter, as of the sound speed in a plasma, it must vary as in the other medium as the pressure or temperature changes I could not find a actual number, but I can assume that the speed in it is higher still to many magnitude. if you have the knowledge to figure out the formula here it is:

plasma_sound_formula-300x20

Baryonic matter, is anything that constitutes our visible universe, which is about 4% of its composition. The bulk of the universe is made with 23% Dark Matter, and since we do not know what it is made of, we do not know how sound waves behave in it; but since sound is so instrumental in the shape of the universe, there is no reason to think that it is not affected as well. The rest, 73%, is made up of Dark Energy, an even more puzzling phenomena but on which sound could help shed light.

All this brings me to the point I want to make: sound waves have an influence on matter of all kinds. They have an elastic or kinetic effect due to the slow rate of their frequencies, compared to the electromagnetic spectrum (light, etc.) which, due to the shortness of their frequencies only have influences at the atomic level.

What is the loudest sound ever created in this universe? Well, it has been very adequately named, as we are all calling it the “Big Bang”– just think about what it means!

The Big Boom, right? But we all have seen those science fiction movies with silent explosions, as being in space, there is no medium, so no sound. That is right, except for the fact that in the case of the Big Bang, it is sound that created the empty space. The Big Bang was infinite pressure, so sound must have traveled infinitely fast, its wave spreading to every corner of the young universe, pushing matter with its peaks and valleys in clumps and creating voids, engineering stars, galaxies and galaxy clusters, and somewhat its own demise– empty space or vacuum.

Now, sound is left vibrating, isolated in the islands of matter that dot the universe, where the original Boom still resonates from all directions. It can be measured and it has a name. It is called the “Baryon Acoustic Oscillation” or BAO. The following is a quote from an article by Richard Panek in the February 2009 issue of Sky & Telescope:

‘Early in the Universe, sound waves (“acoustic oscillations”) coursed through the primordial gas, creating peaks at intervals of 436,000 light-years. As the universe has expanded, so has the spacing between these peaks; today they are 476 million light years apart. And because galaxies tended to form on the peaks of these large waves, astronomers can measure galaxy distributions at different eras, allowing them to see how the peak spacing changed over time, and thus how fast the universe has expanded.’

This will help us measure the effect Dark Energy has on accelerating the expansion of the universe, and help predict its ultimate fate… And fittingly this all was discovered about forty five years ago with the use of a giant ear! (see picture below)

cmbhornantnasap

This is only the genesis of the much under-reported fundamental influence that sound plays in our existence that we shall explore in future postings, so tune in (you have no choice).