Sticks and stones may break my bones, but words may too

Introduction

We’ve all heard the famous proverb which this post is named after, and on its own there isn’t much to it. However, I, like we all do sometimes, look at the words being spoken a little too literally, and think to myself – What a wonderful world- that it may be too hasty a conclusion. So, today we will set out together to answer whether this proverb either is a sham or uhhh…. hold on…. or if it will pass our exam (nailed it).

Let me get this out of the way first, we all know that it would be possible with “sound” in general, but we aren’t looking for the shockwave of an atomic bomb or whatever. In this case our main interest is if it could be caused by a sound that we can: a) hear (if our eardrums don’t shatter at least) and b) produce with a reasonable amount of energy. So let’s set out like the third dog, walk away with the bones and start off with how we could actually rattle said bones.

Like music to my ears

The first thing that came to mind was the option of using resonance, like in a tuning fork, to cause it to shake out of control (music makes me lose control and all that). This is because it keeps increases the amplitude of the vibration or in simple terms just makes it stronger. However, every object, not just material, has its own frequency at which it starts to resonate. But, what decides this frequency, also called the natural frequency, and why do objects have it to begin with? Superficially we like to say that the objects resonant frequency is based on its material, shape, length and thickness, but, while true, it goed deeper than that.

When I go all Unga Bunga on one of those tuning forks with my hammer I change the shape of the object temporarily; the metal in the fork is in a higher energy state. The metal lattice has a fixed structure and I shifted it, which takes energy, so the metal moves back to the lower energy state.

So, the vibration happens because you put in potential energy, then gets returned to normal because it becomes kinetic energy, but also has enough of this movement to go beyond that the rest position and shift in the opposite direction. This happens until this dampens due to resistance as heat and SOUND (or just ignore this dampening like all the cool kids, in which case it vibrates perpetually but without releasing sound).

Here we can see that the actual movement in our situation isn’t caused by the one who hit the object but by the bonds within the object forcing it into the lowest energy cost state (what a cheapskate). This means that the strength and shape of these bonds is what decides what this frequency is. This is actually just the same process as what happens with a spring with a wait on it.

I only used examples of hitting objects, but this is also possible via just sound waves in the air, or at least you vocal cords hitting the air, because we’re not living in a fantasy land where we can just will things into existence (sadly). The classic situation is with breaking glass with just your voice, if you have one as lovely as me that is (totally accurate). This can occur because the resonant frequency of glass is actually quite low (compared to other objects, not our voices), which happens because the bonds in the glass are all things considered quite weak and the molecules actually have a lot of movement between them.

But what about our beloved “rigid organ”, as wikipedia describes it, does this too have such a low resonant frequency?

A Bone to pick

To know how to break bone, we must first know what bone to break. For the proverb to be inaccurate, only the weakest bone will need to break due to whatever we say. To acquire this information, i searched for terms like “What is the easiest bone to break in someones body?” and “How much force (in newtons) do I need to break bone”. (Editors note; Hans is now on the FBI watchlist). Generally the weakest in the body (except for my mental fortitude) is the clavicle bone, which resides somewhere in the body. I’m not a biologist and I would’nt know where; go take it up with the tree huggers.

Thanks to some truly groundbreaking resource in bonebreak-ology, which was possible because of a very generous organ donor (No really they used someones body for this), we know that the clavicle has its resonant frequency at 1014 Hz and 1108 Hz.

It has two different dimensions it can vibrate in,  the “coronal plane” and the “axial plane” , of which I definitely know what they are. After “remembering”, and not using google, it has become clear that these are the, very formally named, jumping jacks plane and the hula hoop plane (the directions in which they move). This information was gathered from this, interesting to read and not at all concerning, paper: An experimental modal analysis of clavicle bending modes

Both these frequencies are within range of what humans can both hear and produce (we can hear between 20 and 20 000 Hz), so why don’t our bones break on a daily basis? Well, resonance only causes the amplitude of the vibration to increase, but if this increase itself isn’t enough to cause breakage, nothing happens.

Dampening

If I would keep adding to the amplitude, we would logically conclude that it would eventually break apart no matter how little I add to it. We all know this can’t be the case, so, to replicate reality, we will have to add that pesky resistance. In a vibration, or a wave, this is called dampening, which can be expressed as the percentage of the amplitude that decreases over time.

The dampening for the most relevant plane, the axial plane in our case, is equal to approximately 8% according to that very important research paper I talked about earlier. To make sure that our bone breaks we need to put in at least 8% of what decreases at the point where it breaks. If we do it like this it would gradually increase until the breaking point and then well.. break. It is pretty simple to figure out the time needed for the amplitude to accumulate, which you can do with a recursive formula: you add the 8% of the total each period and subtract 8% of the subtotal each period, but this is physics and not maths, so I won’t bore you with how I did this.

Because the frequency of my beautiful singing would be the same as that of the bones vibrations, we won’t need to do any hard calculations about the speed at which I add energy (or amplitude) versus what leaves.

The results

As always, flashbacks to the post about the breaking point of rock, Sending Cape Canaveral into space with C-moon, it’s a huge pain in the clavicle to get all the experimental data in line, so that I can actually commence my calculations. For my calculations I used the measurements of those of an adult male who has taken in sufficient calcium, enough to make the average skeleton on halloween proud (I know I’m late, just go with it).

I still had to do some research for the data about the clavicle, but also learned a lot about varies clavicle conditions from the medical sites which popped up a long the way (not sure if this is an overal improvement for my anxiety though).

Shenanigans aside, I can now very definitely say (1000% accurately, might I add) that your bones will break if the sound goes above 81 db at 0m from the bones away. This is actually a quite achievable number being about equal to having a power drill right up in your grill, but instead at a frequency of 1108 Hz.

Both these values are, while not as easily done by everyone, quite simple to be replicated by a humans vocal cords, or, to make it even easier, using a speaker.

If this would be applied as my masterful symphony, my magnum opus, it would take a mere 60 milliseconds for someone to succumb to the beautiful melody (its literally just one tone but let me have this okay?) and…. possibly break their weakest bone.

If you are wondering what this chef-d’oeuvre sounds like you could take a look (or a listen) to this video: https://www.youtube.com/watch?v=3aAlFluZuw, made by someone who predicted this blogpost 5 years in advance, and has awaited its arrival (beats me why someone would make this but who cares).

Now, even if you managed, with your epic gamer setup, to play the sound at 81 db you’d have found to your shock, and maybe even dismay, that it has in fact not shattered your bones. This is of course again because I only looked at the bone in isolation (he doesn’t have any friends), so your muscles and skin which dampen or counteract the force acted open them aren’t taken into account.

However, my point still stands and I have again shown my superiority over the English language whom I despise so much, forever solidifying the scientific subjects to be above the languages. I mean what are they even good for? Writing about other things, like this blog? I’m not just salty because I suck at doing the words (please believe me :3).

So yes, words will definitely hurt you, and I’ll make sure of that.

Final remarks

I know this knowledge is to powerful for us, mere mortals, to wield. I should have stopped to think if I should, instead of just if I could, but at least we did some physics along the way.

It’s been somewhat longer since that last post, because we’ve been more busy as of late (and my brother is lazy but don’t tell him you got that from me, (Editors note; seconded)), but we will try to keep a more steady upload schedule in the near future.

So, I’ll see you all next post about a thing that has definitely already been decided