# Ch12s - Chapter 12 Problem Solutions 12.1(a Af = A 1 A 5...

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Chapter 12 Problem Solutions 12.1 (a) 5 5 5 5 1 5 10 120 1 (5 10 ) 120 (120)(5 10 ) 5 10 0.008331 f A A A β β β β = + × = + × + × = × = (b) 3 3 3 3 5 10 120 1 (5 10 ) 120 (120)(5 10 ) 5 10 0.008133 β β β × = + × + × = × = 12.2 (a) 0.15 1 f A A A β β = = + T A β = (i) T = ∞ (ii) 4 3 80 dB 10 1.5 10 A A T = = = × (iii) 15 T = (i) 1 6.667 f A β = = (ii) 6.662 f A = (iii) 6.25 f A = (b) (i) T = ∞ (ii) 3 2.5 10 T = × (iii) 25 T = (i) 1 4.00 f A β = = (ii) 3.9984 f A = (iii) 3.846 f A = 12.3 (a) 1 125 1 f A A A β β = = + 0.0080 β = (b)

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[ ] [ ] (125)(0.9975) 124.6875 124.6875 1 (0.008) 124.6875 1 (0.008) A 124.6875 1 0.9975 49,875 f A A A A A A = = = + + = = = 12.4 (a) 4 4 3 10 100 1 (10 ) 9.9 10 β β = + = × (b) 4 100 ( 0.10) 0.001 0.10% 10 f f f f f dA A dA A A A dA A = = = − = − 12.5 4 4 4 3 0.001 ( 0.10) 5 10 500 5 10 500 1 (5 10 ) 1.98 10 f f f f f dA A dA A A A A A β β = = ×