Hi I have this D'Alembert's question. What I've done seems easy so I wanted to clarify just in case I'm missing something, cus it seems so easy. Second part I don't understand and would appreciate a guidance.
(PART A)
D'Alembert's Solution is:
of the one dimensional wave equation:
with "c" a constant, when the initial conditions are:
Evaluate the solution if F(x)=0 for and
(PART B)
Show the values of z(x,t) for t>0 in different regions of the (x,t)- plane. Show that the value of z(x,t) is continuous for all values of x and t, gives the correct initial value of and as |x|
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SOLUTION TO PART A:
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GRAPH:
Working out region 1:
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Working out region 2:
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Region 2 = 0.
Working out region 3:
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FINAL SOLUTION:
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Thats part a done. As far as I know that's all there is to evaluating the question. Is there anythin else I need to add???
PART B: any ideas on this please?