- #1
snoopies622
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I've having trouble understanding a derivation of the speed of sound waves, which is actually similar to another derivation I found a couple days ago.
Let's suppose the sound is moving through water in a long cylindrical horizontal pipe. The premises of the derivation are
1.) For a given cylindrical slice of water of thickness , the net horizontal (direction of the wave motion) force acting on the water is proportional to the hoizontal pressure gradient times , so
2.) the mass flux through any infinitely thin cylindrical slice is constant, or
And from these premises one can arrive at .
What I don't understand is why the second premise is true, since neither the water density nor water speed is constant. Or perhaps I don't understand the second premise: Is it supposed to be for an infinitely thin slice, or for a cylinder of thickness , or something else?
Thanks.
Let's suppose the sound is moving through water in a long cylindrical horizontal pipe. The premises of the derivation are
1.) For a given cylindrical slice of water of thickness
2.) the mass flux through any infinitely thin cylindrical slice is constant, or
And from these premises one can arrive at
What I don't understand is why the second premise is true, since neither the water density nor water speed is constant. Or perhaps I don't understand the second premise: Is it supposed to be for an infinitely thin slice, or for a cylinder of thickness
Thanks.