# πφ π φ φω ω ```Svar j&auml;mna Ed. 13
15.36 a) Separationen mellan noderna &auml;r 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 vst&aring;nd 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 &times; 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) Avst&aring;ndet &auml;r 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&deg;.
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 &times;
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