I want to be able to measure sound that is made at the beginning of a pipe (eg diameter 200 mm, length 100 meters). This pipe is basically flat. But halfway there is subsidence, in which water stands. At the end, the pipe is dry again. Can I still measure something, or is the sound too much attenuated?
Answer
Your tube will function as a waveguide. Several modes can propagate in a waveguide, with complexity increasing with frequency. Below a certain cutoff frequency (given by f=340/(1.7*D), where D is the diameter of the tube) only one mode can propagate in the tube and that is a plane wave that propagates at a speed of about 340 m /s. So the exact cross-sectional shape of the pipe doesn’t matter then and even if there are cross-sectional changes along the way, it’s of little influence. So below that cutoff frequency, life is very simple. So if the pool of water in the center of the tube just changes cross-section, but doesn’t completely close off the entrance, you can pretend it isn’t there (just make sure your signal doesn’t contain any frequencies above the cutoff frequency).
It’s another matter if the pipe sags to such an extent that the water completely closes off the entrance. At that moment a reflection occurs at the air/water surface (and again at the water/air interface). The magnitude of that reflection depends on the impedance difference of the two media (the impedance is the product of density and speed of sound). Since the impedance of air and water are very different, the reflection is very large. The water acts as a ‘stop’ and blocks almost all noise.
Answered by
Prof Walter Lauriks
Physics Acoustics
Old Market 13 3000 Leuven
https://www.kuleuven.be/
.