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I have done an experiment where I vary the levels of water in a wineglass and record the frequencies it produces which differ depending on the height of the water.

Below you see 1 equation, apparently I can use this equation to mathematically prove my results from my experiment, (this equation has been rewritten from the original equation created by AP french (https://www.nikhef.nl/~h73/tgo/praktgeluid/French1983.pdf)

My first question is: How has this equation been rewritten (where does the 0.2 come from etc. ) and what does the overall equation mean.

My second question is whether the variables that I think they are are actually the variables that they are.

I think the variables are: (could someone please confirm)

h = height of water in the wineglass

H= height of the wineglass

R= radius of the glass

a= thickness of glass

f0= frequency of wineglass when empty

R = the radius of the glass

my problem is that the radius of the glass differs it is bigger in the middle etc. so which radius do I use???

for now with the calculations I've done I've just used the radius of the glass at the top of the glass.

Another question is graph related my graph currently looks something like this:

I've also read that its possible to plot two parts of the equation above against each other which would create a linear relationship in a graph and this would then prove the equation again. (could someone explain how to do this and why this works?) (this is also explained in ap french document i have posted url to earlier but i don't understand what is written there.)

(ignore the stuff in the middle this is not my graph)

Finally I understand that the reason for the frequency to decrease has to do with nodes and antinodes and standing waves. basically the glass vibrates and the water within the glass vibrates with it. And this has to do with kinetic energy etc.

Below you see 1 equation, apparently I can use this equation to mathematically prove my results from my experiment, (this equation has been rewritten from the original equation created by AP french (https://www.nikhef.nl/~h73/tgo/praktgeluid/French1983.pdf)

My first question is: How has this equation been rewritten (where does the 0.2 come from etc. ) and what does the overall equation mean.

My second question is whether the variables that I think they are are actually the variables that they are.

I think the variables are: (could someone please confirm)

h = height of water in the wineglass

H= height of the wineglass

R= radius of the glass

a= thickness of glass

f0= frequency of wineglass when empty

R = the radius of the glass

my problem is that the radius of the glass differs it is bigger in the middle etc. so which radius do I use???

for now with the calculations I've done I've just used the radius of the glass at the top of the glass.

Another question is graph related my graph currently looks something like this:

I've also read that its possible to plot two parts of the equation above against each other which would create a linear relationship in a graph and this would then prove the equation again. (could someone explain how to do this and why this works?) (this is also explained in ap french document i have posted url to earlier but i don't understand what is written there.)

Finally I understand that the reason for the frequency to decrease has to do with nodes and antinodes and standing waves. basically the glass vibrates and the water within the glass vibrates with it. And this has to do with kinetic energy etc.

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