Constructing a Tubular Bell Array: Solving the Wave Equation

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To construct a tubular bell array, the wave equation for tubes needs to be established, similar to that for strings, but with specific considerations for the tube's geometry. The velocity of propagation in the tubes depends on the material properties, specifically the density and elasticity of the aluminum or copper used. Once the wave equation is formulated, it can be used to determine the frequencies required for standing waves in the tubes. Understanding how these factors interact is crucial for achieving the desired sound quality. The discussion emphasizes the importance of accurately defining the wave equation to successfully build the tubular bell array.
ELESSAR TELKONT
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I have the next theoretical-practical problem. I have to build a tubular bell array (like that at symphonic orchrestas) with tubes (not rods) of aluminium or copper. The principal problem I have is I don't know how to state the wave equation for a tube (I have done it for a string). How I do it?

When I have the wave equation stated I must get the frecuencies to get a standing wave. Obviously this is what I want.

Could you help me?
 
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If the bells are open at both ends, the wave equation is the same as for strings.
 
Ok but of what quantities the velocity of propagation depends on that's my problem.
 
The velocity of propagation is the velocity of sound.
 

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