# Sound pitch of glass with water

I have a glass (made from glass) at room temperature. I poured very hot tea in it and started stirring. No extra tea is poured in the glass. When hitting the glass with the spoon, I noticed the pitch of the ringing sound changed as the glass itself got hotter and hotter.

Why is that? Why is the resonance of the glass change with it's temperature?

It's probably the temperature of glass itself. Speed of sound in solids depends on the elastic moduli (the choice of the modulus depends on the polarization of sound - in this case, it's mostly transverse motion, as you are observing glass oscillation). The change of the density of the hot air may also contribute.

Possible contributions and why they can be excluded:

• density and thickness of glass: thermal expansion coefficients aren't that big (a few $10^{-6}K^{-1}$).
• change of water properties: not really, the part of the glass that interfaces water doesn't vibrate all that much, as water has a lot of intertia.
• elastic moduli: maybe... glasses are known to get softer gradually with increasing temperature. Can't find numbers now, but probably contributes more than thermal expansion.
• hotter air is less dense. So it's essentially the same effect as breathing helium. However, resonant frequency of the glass is not that much affected by the air density (vocal cords are a different thing).

From all this, #3 seems the most likely candidate.

EDIT: now that I think of it, it's possible that while the expansion itself doesn't do that much, stress that is created during nonuniform expansion changes the elastic response (it's pre-stressed, the same reason the glass may break when heated nonuniformly). So... it could still be elasticity, but maybe through a slightly different process than just getting softer... you can test this by waiting for the temperature to equilibrate and trying again.

I'm assuming that you're talking about frequency while keeping the amount of water constant (and the surface at rest).

Glass contracts when heated. This means the individual molecules compact as they meet the heat catalyst. This is one reason for the resonance difference. But also: If you take two separate glasses and fill them at different levels of room temperature water you will find they have different resonant frequencies as well. So in your heated liquid experiment as the glass contracts it is actually changing the spatial mass ratio between glass and water, like in the two-glass room temperature example, which then changes the resonance slightly also.