# Sol-Ch16 - CHAPTER 16 E xercises 1 = c/f(a 188 m to 546 m(b...

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Exercises 1. λ = c/f : (a) 188 m to 546 m; (b) 2.78 m to 3.41 m 2. ω = 10π/9 RAD/S, At the rim v = ω r = π/6 m/s. f = v/ λ = (π/6 m/s) (1.2 × 10 –3 m) = 436 Hz. 3. (a) λ =4 cm, thus f = v/ λ = 10 Hz; (b) Δ Φ = (Δx/Δ λ ) = 2π = 5π/4 ; (c) T = 1/10 s, Δt = (60/360) T = 1/60 s; (d) –(∂y/∂t) max = – ω A = –1.26 m/s 4. (a) ω = 10π/9 rad/s. At the rim v = ω r = 10π(0.145) /9 =0.506 m/s. Signal T = 10 –4 s. In this time Δs = vT = 5.06 × 10 –5 m; (b) λ = v s T = 3.4 cm 5. Δt = Δx (1/v s – 1/v p ), thus Δx = 1440 km 6. F = v 2 µ = 13.3 N 7. m = FL/v 2 = 0.563 kg 8. F 2 /F 1 = (v 2 /v 1 ) 2 , thus F 2 = 15(45/28) 2 = 38.7 N 9. (a) λ α (F) 1/2 /f, thus f 2 = (2) 1/2 f 1 ; (b) v α (F) 1/2 , so v 2 = (2) 1/2 v 1 10. (b) It takes Δt = 0.5 s to reach the peak, thus, ∂y/∂t = (1 cm)/(0.5 s) = 2 cm/s, up 11. (b) It takes Δt = 1 s to go from the peak to zero, thus, ∂y/∂t = 1 cm/s, down 13. f(x + vt) = (2 × 10 –3 )/[4 – (x + 12t) 2 ] m 14. v = 1.2 cm/0.3 s = 4 cm/s, ω = 2πv/ λ = 8π/7.5 , Φ = π/2. y = A sin(kx – ω t + Φ ) = 2 cos(2πx/7.5 – 8πt/7.5) cm 15. (a) ∂y/∂x = kA cos (kx – ω t) ; CHAPTER 16

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(b) (∂y/∂t) max = v (∂y/∂x) max 16. (a) 2.5 m/s ; (b) (Δ Φ /2π) λ = λ /3 = 10π/3 = 10.5 cm 17. (a) (∂y/∂t) max = ω A = (2π)(2.4) = 4.8 π cm/s = 15.1 cm/s; (b) ∂y/∂t = 4.8 πsin (0.75π/20 – π/2) = –15.0 cm/s; (c) a max = ω 2 A = 94.7 cm/s 2 ; (d) a = – ω 2 Acos(0.75π/20 – π/2) = –11.1 cm/s 2 18. (a) f = ω /2π = 1.91 Hz; (b) v = ω /k = 5 cm/s; (c) A = 0.03 cm; (d) ∂y/∂t = + ω A sin[(2.4)(15) – (12)(0.2) +0.1] = 0.272 cm/s; (e) amax = ω 2 A = 4.32 cm/s 2 19. a, b, d, e 20. (a) Δ Φ = 2π(Δx/ λ ) = 2.51 rad; (b) Δ Φ = 2π(Δx/T) = 11 rad (or 11 – 2π = 4.72 rad) 21. (a) λ = 2π/k = 15.7 cm, Φ = 0.8 rad; (b) T = 2π/ ω = 0.126 s; (c) A = 0.02 cm; (d) v = ω /k = –125 cm/s; (e) ∂y/∂t = ω Acos(0.4 + 25 + 0.8) = 0.483 cm/s 22. (a) λ = 2π/k = 10π =31.4 m (b) T = 2π/ ω = π = 3.14 s (c) v = ω /k = 10 m/s 23. y = 0.03 sin(2πx/0.025 + 2πt/0.01 + Φ ) = 0.03 sin(80πx + 200 πt + Φ ) y = (0, 0) = –0.02 m = 0.03 sin Φ , so Φ = –0.730 rad, –2.301 rad. Since v > 0, it means cos
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## This note was uploaded on 11/09/2011 for the course EE EE taught by Professor Ee during the Spring '11 term at National Chiao Tung University.

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Sol-Ch16 - CHAPTER 16 E xercises 1 = c/f(a 188 m to 546 m(b...

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