# Is there an equation to relate a glass's frequency to its mass when it's struck with a spoon?

The mass therefore would be changing because I am pouring in water and testing the frequency at different volumes. Obviously as the volume increases the mass increases and the frequency decreases.

How would I exactly model this with an equation?

Perhaps using the equation for a simple harmonic oscillator: $$\left[\text{frequency}\right] ~=~ 2 \pi \sqrt{\frac{\left[\text{stiffness constant}\right]}{\left[\text{mass}\right]}} \,.$$ But can the stiffness constant really be applied to a material like glass, since its so rigid and brittle and not like a spring?

So does anyone have any suggestions?

• I'm not sure at all if the simple harmonic oscillator equation would apply directly here (I'm thinking not; but I don't know enough about it's assumptions to really say); but glass definitely does have a stiffness associated with it. It's also pretty well behaved in that regard, in the sense that it's stiffness is quite linear, so it actually has a constant that doesn't vary much with applied load.
– JMac
Commented Mar 7, 2019 at 20:51