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_0 to become ?_0ϕ(vt-x).  Prove that the velocity u (at time t and distance  x from the origin) is given by

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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_0 to become ?_0ϕ(vt-x).
 Prove that the velocity u (at time t and distance
 x from the origin) is given by

 

V +
(u。 - v) (vt)
o(vt - x)
Transcribed Image Text:V + (u。 - v) (vt) o(vt - x)
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