Question

I would like to consider the sound incident to a water filled pipe wall. I think the pipe wall is typically considered as a rigid wall boundary, it means all the incident wave is reflected. Is this assumption is correct in real world? I think if the sound inside the pipe is large, we can hear the sound from outside the pipe. In practical, what kind of boundary condition should be assumed for the pipe wall?

Answer 1

The assumption that a water-filled pipe wall acts as a rigid wall boundary leading to complete reflection is not fully accurate. Reflection and transmission of sound depend on the acoustic impedance and boundary conditions, with varying outcomes whether the boundary is fixed or free to move.

Step-by-step explanation:

When considering the sound incident to a water-filled pipe wall, the rigid wall boundary assumption that all the incident wave is reflected is not entirely accurate. In the real world, pipe walls are not perfectly rigid and will exhibit some transmission of sound due to the physical properties of the material and the boundary conditions. Specifically, when sound waves encounter a boundary, such as a pipe wall, there are reflections and transmissions that occur. The amount of reflection and transmission depends on the acoustic impedance of the two media. The acoustic impedance, Z, is given by Z = ρv, where ρ is the density of the medium and v is the speed of sound through the medium. A greater difference in acoustic impedance results in more reflection and less transmission.

A fixed boundary condition occurs when the boundary cannot move, leading to an inverted reflection of the wave. In contrast, a free boundary condition occurs when the boundary can move, where the reflected wave is in phase with the incident wave. Considering the acoustic properties of materials and boundary conditions is essential for accurately determining the sound behavior in engineering and physics problems.