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
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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