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So, this morning I woke up and remembered something I discussed about with one of my friends:

Can human voice really break a wine glass?

So I looked it up and after checking many websites and some videos the answer was:

Yes, but it's not easy.

From what I've learned, reaching the natural frequency of glass is not hard for human voice, the real problem is the volume, and many experiments just had to amplify the voice in order to get a positive result while very few others succeeded just by natural means if you will. Other important factors that were mentioned: the thickness of the glass (I read that it's even easier if it's a crystalline material) and the presence of imperfections, such as micro-fractures inside it.

So what I'm asking is:

  1. what are the laws behind that?
  2. I know it is connected to the resonance phenomenon but can one express this mathematically such that e.g. the thickness of the glass and its natural frequency are related with the necessary volume?

My guesses for influencing factors:

  • Shape of the glass
  • The specific chemical compounds involved

but maybe they are part of the natural frequency of the glass.

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  • $\begingroup$ I didn't write the question like that but it's okay I guess.. $\endgroup$ – user77111 Apr 12 '15 at 12:43
  • $\begingroup$ Feel free to undo the edit or reformulate your questions again if you are unhappy, there's no problem. $\endgroup$ – Phonon Apr 12 '15 at 13:11
  • $\begingroup$ Is it automatic? Nono I'm fine with it I think but maybe I just pressed something I didn't know ahah $\endgroup$ – user77111 Apr 12 '15 at 15:02
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There are just two requirements, 1) correct frequency, and 2) sufficient amplitude. The correct frequency is, the resonant frequency of the glass cup (pane, cube, etc.). You will know you have sufficient amplitude, when the glass breaks! Both requirements will vary, depending on the material, shape, dimensions of the object, and other variables.

If you run experiments, hold constant as many of the variables as possible by using the same manufacturer, same glass material, same shape, etc.. Take one object, determine its resonant frequency and the amplitude required to break it. Get another item and repeat. Change one variable and repeat. Hopefully you will be able to come up with some empirical constants which then will be used to predict the frequency and amplitude at which a given object will break.

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  • $\begingroup$ EXACTLY WHAT I WANTED TO DO! Thank you so much for confirming what I thought. I aslo thought that maybe I should study Before the resonant frequency of the glass to see how it varies according to the diamater, shape and composition of the glass $\endgroup$ – user77111 Apr 15 '15 at 15:29
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First: what frequency should you hit? There are many, many different factors at play in determining the natural frequency of an object I know from experience. These are (not limited to): Thickness, density, elasticity modulus (you'll need two of those, e.g. Young's Modulus and Poisson Ratio), and of course shape. I'm not aware of any papers publishing a relation between these variables and frequency.

Then, you need to take damping into account; this can again be influenced by many things. For example, the roundness of the glass (even a slightly elliptical shape will produce a 'beating' sound like tubular bells/chimes) is important. Compare with trying to 'whistle' with a soda bottle; as soon as you dent it even a little, the tone disappears immediately. Then, there is the shape, where generally rounder will make for less damping, and also for a stronger glass.

Now, to break a glass, you need to add as much energy as possible, with as little as possible dissipating due to damping, so that the internal 'vibration' energy becomes larger than the binding energy of the weakest bit of glass. Here, we run into a bit of trouble; except for thickness, you can generally say that properties that allow for greater resonance, also make the glass stronger. For example, a glass will break on discontinuities in the glass, but these discontinuities will also continuously dissipate energy long before the glass breaks; energy concentrations will form on 'fancy' shapes in your glass, but these will again allow for less resonance.

So really, the only thing that we can say for sure, and which a 5-year old would also answer, is that thinner is better. For all the other variables, you will need to come up with an approximation. You could do FEM analysis, but I would rather just use experimentation. This will mean breaking a LOT of glasses, and asking a manufacturer for glass samples to test all the other properties of your glass; there are probably papers out there that have this information based on chemical composition and manufacturing process. Then, I guess, you could come up with some factor that captures the shape of the glass in your empirical relations (a bit like the drag coefficient $c_d$ in $\frac{1}{2}c_d\rho v^2$). And then, if you have WAY too much time on your hand, you could try and predict this factor for other shapes. If you do, please publish your results for the world to enjoy :)

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  • $\begingroup$ Thank you so much. That's what I thought in second istance: many factors I forgot. And yes I'd like to try and perform this experiment, but I'd need some equipment. Without any doubt I will If I do. $\endgroup$ – user77111 Apr 12 '15 at 12:44
  • $\begingroup$ A good starting point would just be a DB-meter and (guitar) tuner (both come on smartphones) and a sound-generator (there are sine wave generators on the internet, so really you only need a smartphone or two and a speaker set), and with a bit of luck you can find a wine glass manufacturer that can provide you with data about their glass used (which you can cross-reference with other sources), and some of their rejected glasses on which you can do most experiments - then you need only one batch of good glasses to 'scale' your results. $\endgroup$ – Sanchises Apr 12 '15 at 12:51
  • $\begingroup$ Thank you so much for your advise! Yes I think I could manage to do that after all! $\endgroup$ – user77111 Apr 12 '15 at 12:59
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Any structure that leads to a high Q system (the glass) will work and the trick is precisely matching the resonant (natural frequency ). By mounting the glass in a clamp that dissipates energy at a lesser rate than the sound energy that feeds it, the glass is doomed regardless of thickness or lack of imperfections. If the rate of energy input exceeds the rate of dissipation, the resonance will feed on it and ... disaster.

An inexpensive way to detect when the natural frequency is matched is to place a ping pong ball in the glass.

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