# 16 - E xercises 1 3 = c/f(a 188 m to 546 m(b 2.78 m to 3.41...

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Exercises 1. λ = c/f : (a) 188 m to 546 m; (b) 2.78 m to 3.41 m 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 10. (b) It takes Δt = 0.5 s to reach the peak, thus, ∂y/∂t = (1 cm)/(0.5 s) = 2 cm/s, up 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 19. a, b, d, e 22. (a) λ = 2π/k = 10π =31.4 m (b) T = 2π/ ω = π = 3.14 s (c) v = ω /k = 10 m/s 26. (a) λ = 2π/k = 12.6 cm, f = ω /2π = 4.77 Hz, v = ω /k = 60 cm/s (b) ∂y/∂t = –120 sin(0.5x)sin(30t) = 101 cm/s 36. λ 2 = 2 λ 1 /3, so f 2 = 1.5 f 1 = 480 Hz 40. Both, f(x – vt) 75. y = 2Asin(8.4x + π/6)cos(50t). nOdes are at (8.4x + π/6) = nπ, thus x =0.312 m, 0.686 m. 76. f = v/2L = (F/µ)

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16 - E xercises 1 3 = c/f(a 188 m to 546 m(b 2.78 m to 3.41...

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