# Can the fullness of a cylinder of water be determined by its frequency

#### tsuwal

1. Homework Statement

We have high cilinder with height h a filled with water up to the height L<h and air in the rest. We hit the cylinder and listen to the frequency of its sound. How can we determine L in function of h, the frequency of the noise, the speed of sound, ...

2. Homework Equations

3. The Attempt at a Solution
Maybe the sound has something to do with the harmonics on a string. Is the frequency =velocity of sound/(2*(h-L))?

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#### haruspex

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You don't say whether it is hit above or below the water line.
In general this could be pretty complex. The cylinder will have several modes of vibration that are affected by the water depth. There'll be a bulk vibration within the water-filled part, vibration in the air column, and vibrations in the cylindrical wall above the water (both vertically and radially). Pick one that you think will be affected.

#### tsuwal

if we made a simplification like just assmuning the vibration of the air, could qe solve it?

#### haruspex

Homework Helper
Gold Member
2018 Award
if we made a simplification like just assmuning the vibration of the air, could qe solve it?
Yes, but to complete the picture for that vibration we'd need to know whether the cylinder is open or closed at the top. Do you know about nodes, antinodes, standing waves in pipes...?

#### tsuwal

yes. the cylinder is closed at the top

#### haruspex

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Gold Member
2018 Award
yes. the cylinder is closed at the top
OK, so how many wavelengths can be in the air column in general?

#### tsuwal

nodes are located at the extremeties, so using my variables 2(h-L)/n But i don't know if experimentally this can be verified...

#### haruspex

Homework Helper
Gold Member
2018 Award
But i don't know if experimentally this can be verified...
I don't understand why you are looking for experimental verification. I thought the idea was to use theory (which could be verified by experiment if required) to come up with a procedure for judging L from the sound.

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