Constructing a Bessel Function from a vibrating surface of water

In summary, the speaker is working on a project to construct the Bessel function of a vibrating surface of water in a cylindrical tank. They plan to use sound sensors to measure distance vs time data for a specific ρ and Θ in cylindrical coordinates, but are concerned about the accuracy of the data. They are considering purchasing a laser distance measuring device for more precise data. They also mention the possibility of using the Bessel function to construct the waveform of the signal vibrating the water, which could have interesting applications. They refer to Seth Putterman's work as a reference for this type of measurement.
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Erenle
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Hey everyone, I'm currently working on a project to construct the Bessel function of a vibrating surface of water in a cylindrical tank. My basic idea is to have a way of observing a point on the surface of water and obtain distance vs time data to that point (which will rise and fall with wave crests and troughs) for a specific ρ and Θ in cylindrical coordinates. All I have on hand with me are a few sound sensors, but these would probably give very inconsistent data as I can't be sure how large of an area they're measuring on the surface of the water. So I was thinking of purchasing a distance measuring device that utilizes a laser, as it would give me much more precise data. I was curious if anyone had knowledge of where I could get some kind of laser sensor. I was also curious in the long run if it could be possible to construct the waveform of the signal vibrating the water after obtaining the Bessel function, because that could have interesting applications.
 
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Lots of people have performed this type of measurement, I am most familiar with Seth Putterman's work:

http://www.me.ucsb.edu/~ceweb/faculty/pine/papers_pdf/1997fPuttrScience.pdf
 
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1. What is a Bessel function and how is it constructed from a vibrating surface of water?

A Bessel function is a mathematical function that describes the oscillating pattern created by a vibrating surface of water. It is constructed by mapping the displacement of the water surface over time and using this data to calculate the amplitude and frequency of the oscillations.

2. What are the practical applications of constructing a Bessel function from a vibrating surface of water?

The Bessel function is useful in many fields, including acoustics, optics, and fluid dynamics. It can be used to study the behavior of vibrating surfaces, such as drum heads or cymbals, and to model sound waves in different mediums.

3. How does the shape of the vibrating surface of water affect the resulting Bessel function?

The shape of the surface of water, whether it is circular, rectangular, or irregular, will affect the resulting Bessel function. Different shapes will produce different patterns and frequencies of oscillation, which can be analyzed using mathematical techniques.

4. Can Bessel functions be constructed from other types of vibrating surfaces besides water?

Yes, Bessel functions can be constructed from any type of vibrating surface, such as a membrane or a string. The principles and techniques used to construct the Bessel function from a vibrating surface of water can be applied to these other systems as well.

5. How can Bessel functions be used to understand and predict the behavior of vibrating systems?

By analyzing the Bessel function of a vibrating system, scientists can gain insight into the system's properties, such as its natural frequency and damping. This information can then be used to predict how the system will behave under different conditions or when subjected to external forces.

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