It is well known that the frequency dispersion curve of a pipe depends on the wall thickness and the diameter of the pipe. Whether there is a situation where the diameter and thickness of pipes are different but the frequency dispersion curve is identical (for example, the first type of pipe has a small diameter and a small thickness, and the second type of pipe has a large diameter and a large thickness). When is the frequency dispersion curve the same and the ratio of thickness to diameter the same?
Dear Sen deng
I did some research for you.
The frequency dispersion curve of a pipe is primarily dependent on its dimensions, material properties, and boundary conditions. While pipes with different dimensions and thicknesses may have similar frequency dispersion curves, it is unlikely that two pipes with significantly different dimensions and thicknesses would have identical dispersion curves.
However, it is possible for two pipes to have the same frequency dispersion curve if the ratio of their thickness to diameter is the same. This is because the ratio of thickness to diameter affects the stiffness and mass distribution of the pipe, which in turn affects the speed of sound waves traveling through the pipe. If two pipes have the same thickness-to-diameter ratio, they will have similar stiffness and mass distributions, leading to similar dispersion curves.
Therefore, if the ratio of thickness to diameter is kept constant, then pipes with different diameters and thicknesses can have similar frequency dispersion curves. However, it is important to note that other factors such as material properties and boundary conditions can still affect the dispersion curve, so the pipes may not be exactly identical.
Mathematically,
The frequency dispersion curve of a pipe is a graph that shows the relationship between the frequency of a sound wave and its propagation velocity through the pipe. It is determined by various factors, including the dimensions of the pipe, material properties, and boundary conditions.
The dimensions of a pipe, including its diameter and thickness, affect the stiffness and mass distribution of the pipe. The stiffness and mass distribution, in turn, affect the speed of sound waves traveling through the pipe, and thus, affect the frequency dispersion curve.
Material properties such as density, Young's modulus, and Poisson's ratio also affect the speed of sound waves in a pipe. Different materials have different acoustic properties, which affect the frequency dispersion curve.
Boundary conditions, including the type of termination and the presence of any obstructions or discontinuities, can also affect the frequency dispersion curve.