hw5_soln - Problems from Strauss, 2.1: # 3: The disturbance...

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Unformatted text preview: Problems from Strauss, 2.1: # 3: The disturbance will reach the flea after time t = p ρ T ( l 4- a ). # 5: As in the hint we have: u ( x, t ) = 1 2 c { length of ( x- ct, x + ct ) ∩ (- a, a ) } When t = a 2 c : u ( x, t ) = 1 2 c { length of ( x- a 2 , x + a 2 ) ∩ (- a, a ) } = 1 2 c × a | x | ≤ a 2 3 a 2- | x | a 2 ≤ | x | ≤ 3 a 2 | x | ≥ 3 a 2 When t = a c : u ( x, t ) = 1 2 c { length of ( x- a, x + a ) ∩ (- a, a ) } = 1 2 c × 2 a- | x | | x | ≤ 2 a | x | ≥ 2 a When t = 3 a 2 c : u ( x, t ) = 1 2 c { length of ( x- 3 a 2 , x + 3 a 2 ) ∩ (- a, a ) } = 1 2 c × 2 a | x | ≤ a 2 5 a 2- | x | a 2 ≤ | x | ≤ 5 a 2 | x | ≥ 5 a 2 When t = 2 a c : u ( x, t ) = 1 2 c { length of ( x- 2 a, x + 2 a ) ∩ (- a, a ) } = 1 2 c × 2 a | x | ≤ a 3 a- | x | a ≤ | x | ≤ 3 a | x | ≥ 3 a Similar formulas can be developed for t = 5 a 2 c ....
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hw5_soln - Problems from Strauss, 2.1: # 3: The disturbance...

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