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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 uo to become poo(vt - x). Prove that the velocity u (at time t and distance x from the origin) is given by + a (uo - v) & (vt) o(vt - x)

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 uo to become poo(vt - x). Prove that the velocity u (at time t and distance x from the origin) is given by + a (uo - v) & (vt) o(vt - x)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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。 to become poo(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: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。 to become poo(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)
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