A pulse (gas) travelling along a fine straight  uniform tube filled with gas causes the density  at any time t and distance x from the origin   where the velocity is u\index{0} to become ?\index{0}ϕ(vt-x).  Prove that the velocity u (at time t and distance  x from the origin) is given

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Q: the value i get from step 1 is 1166.675705.

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