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Svar jämna Ed. 13 15.36 a) Separationen mellan noderna är 15,0 cm b) λ = 0,30 m, A = 0,425 cm, v = 4 m/s c) Maxhasighet: 0,71 m/s, Minhastighet 0 m/s d) Kortaste vstånd mellan nod och antinod: 7,50 cm 15.68 b) v y = ωA sin( kx − ωt + φ ). c) No; φ = 7π 4 (samma som φ = - π 4) d) To identify φ uniquely, the quadrant in which φ is must be known. In physical terms, the signs of both the position and velocity, and the magnitude of either, are necessary to determine φ (within additive multiples of 2π ). 15.78 a) Lmax = 0.40 m. rmin = 6,4 × 10 −4 m. b) f 1 = 376 Hz. 16.20 a) 6.0 dB. b) increase of 12 kids 16.34 a) The points of destructive interference would be at x = 0.58 m, 1.42 m. b) Constructive interference would be at the points x = 0.17 m, 1.00 m, 1.83 m. c) The positions are very sensitive to frequency, the amplitudes of the waves will not be the same (except possibly at the middle), and exact cancellation at any frequency is not likely. Also, treating the speakers as point sources is a poor approximation for these dimensions, and sound reaches these points after reflecting from the walls , ceiling, and floor. 16.60 a) pmax = 1,144 x 10-2 Pa b) A =7,51 x 10-9 m c) Avståndet är 62,8 m 16.70 a) 9.01 m, 2.71 m, 1.27 m 0.53 m and 0.02 m b) 4.34 m, 1.84 m, 0.86 m, 0.26 m c) Yes, the frequency is 86 Hz 33.12 a) θ water = 25.5°. b) No dependence 33.20 A = 404 m2 33.36 32,3 W/cm2 33.42 λ ′ = 196nm ≈ 200nm. 33.48 4,4 m from the edge of the pool. 34.30 a) s = 0.0741 m b) The image is inverted c) f = 0.0732m, and the lens is converging. 34.44 y ′ = 39.0mm, so it will not fit on the 24-mm × 36-mm film. 34.64 M = −19.0. 34.92 a) s1 = 14,20 cm, s2 = 3,80 cm b) m1 = -0,27, m2 = -3,74, The negative sign shows that the images are inverted. 34.94 a) b) i. The image from the lens is 51.3cm, to the right of the lens. Then image formed by light reflected in the mirror and then imaged by the lens is also 51,3 cm to the right of the lens. ii. Both images are real iii. The image formed by the lens is inverted. The image formed by both mirror and lens is erect. 35.22 a) 0,888 mm, b)0,444 mm 35.24 a) φ = 4.52rad. b) I = 0.404 I 0 . 35.46 x0 = 760.5 m x1 = 219.0 m x2 = 90,0 m x3 = 20,0 m 35.60 a) d/λ = 1,53 b) θmin= 14,9o