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In The Adventures of Tintin, an opera singer (the Milanese Nightingale) broke a bulletproof glass case using her voice. Is that scientifically possible?

From the Wikipedia page, a typical bulletproof glass

is usually made from a combination of two or more types of glass, one hard and one soft. The softer layer makes the glass more elastic, so it can flex instead of shatter.

When they did it on Mythbusters, the singer had to stand really close to the glass that is so thin for it to break. Any thoughts on whether the movie scene is even humanly possible?

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This must be impossible, even for lady Castafiore with her earthquake voice. For a glass to break by sheer sound you need to produce a tone equal to the glass's natural frequency - the frequency at which a body vibrates with the least amount of energy. In other words: there you get the most vibration with a minimum of effort. This is also called resonance.

However, it is much harder to create resonance in mixed materials because each component has a different fundamental frequency. So two layers of different types of glass will effectively prevent resonance.

Of course, apart from that the mere thickness of the material will be a problem for our Nightingale.

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