Can a Wineglass Shatter from Two Notes?

[pkc111]

pkc111 Says: 10:09 PM Y



If a wineglass can be made that shatters when a loud enough pure high C is played (because the resonace frequency of the winegalss is a high C).If a pure high C (just loud enough to shatter the glass) and an F (same volume) were played at the same time, would the wineglass shatter ?

Thanks

Quote | Reply

 

[danR]

pkc111 Says: 10:09 PM Y



If a wineglass can be made that shatters when a loud enough pure high C is played (because the resonace frequency of the winegalss is a high C).If a pure high C (just loud enough to shatter the glass) and an F (same volume) were played at the same time, would the wineglass shatter ?

Thanks

Quote | Reply

I will call it 'yes'. There are going to be additive peaks and troughs that will drive the glass past the failure strength. IMO.

 

[Fewmet]

I will call it 'yes'. There are going to be additive peaks and troughs that will drive the glass past the failure strength. IMO.

That seems plausible, but I am wrestling with whether any points on the glass would shift to reduce overall stress despite the greater amplitude experiences by some parts of the glass. http://zonalandeducation.com/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html" (if you click on the first and third boxes to display the equivalent of F and then C) makes it look like that won't happen on a d 2D string. I am not confident of my ability to mentally extend this to three dimensions.

It seems like you could craft a neat max-min calculus problem out of this situation.

 

[danR]

That seems plausible, but I am wrestling with whether any points on the glass would shift to reduce overall stress despite the greater amplitude experiences by some parts of the glass. http://zonalandeducation.com/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html" (if you click on the first and third boxes to display the equivalent of F and then C) makes it look like that won't happen on a d 2D string. I am not confident of my ability to mentally extend this to three dimensions.

It seems like you could craft a neat max-min calculus problem out of this situation.

My gut reaction is that if the original sine wave was driving the system just to the point of failure, then the velocity of a peak formation would be even faster than the glass' ability to shift the stress in the first instance, and when glass fails, it's incredibly fast.

 

[HallsofIvy]

You are talking about solving a d.e. of the form
$$\frac{d^2x}{dt^2}+ a^2x= sin(at)+ sin(bt)$$
with the 'sin(ax)' being the "high C" and sin(bx) the "F"

The general solution would be
$$x(t)= Ccos(at)+ Bsin(at)- \frac{1}{2a}t cos(at)+ \frac{1}{b^2+ a^2}sin(at)$$

The multiplied "t" in the third terms is the "resonance" that causes the crystal to break. It is the "superposition" property- the solutions from the two separate waves add. Since the solution for the "high C" alone causes x to be unbounded, so will the superposition of the two solutions.