How Does Liquid Volume in a Soda Bottle Affect the Sound Frequency Produced?

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The discussion revolves around determining the volume of liquid in a soda bottle based on the sound frequency produced when blown into. A specific example is given where a 20cm high bottle produces a sound of 455Hz. Participants express uncertainty about the equations needed for the calculation. One user attempts a solution but arrives at a result of 0.018, which they doubt is correct. The conversation highlights the relationship between liquid volume, sound frequency, and the dimensions of the bottle.
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1. A child blows on a 20cm high soda bottle, and it creates a sound of 455Hz, how much liquid is inside the bottle?


2. not nsure about the equations



3. i attempted a solution, but all came out to something along the lines of 0.018

i don't think that's right
 
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A child blows on a 20cm high soda bottle, and it creates a sound of 455Hz, how much liquid is inside the bottle?

Equation is 1/4*V*1/f = L
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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