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Bộ tài liệu bài tập tham khảo môn vật lý bậc đại học bằng tiếng anh Chapter 15 | 15.1 a The period is twice the time to go from one extreme to the other and v f X X T 6.00m 5.0s 1.20ms. or 1.2m sto two figures. b The amplitude is half the total vertical distance 0.310 m. c The amplitude does not affect the wave speed the new amplitude is 0.150 m. d For the waves to exist the water level cannot be level horizontal and the boat would tend to move along a wave toward the lower level alternately in the direction of and opposed to the direction of the wave motion. 15.2 f X v f v ISOO s 1.5 x 106 Hz X 0.001m 15.3 a X v f 344 m s 784Hz 0.439 m. b f VX 344 m s 6.55 x 10 5 m 5.25 x 106 Hz. 15.4 a Denoting the speed of light by c X f and 3.00x108 m s r rr i 3.00x108 m s 0-7 ------ 556m. b ------------------- 2.87 m. 540x103 Hz 7 104.5x106 Hz 15.5 a Xmax 344 m s 20.0Hz 17.2 m Xmin 344 m s 20 000Hz 1.72 cm. b Xmax 1480 m s 20.0Hz 74.0 m Xmin 1480 m s 20 000Hz 74.0 mm. 15.6 Comparison with Eq. 15.4 gives a 6.50mm b 28.0cm c f t _L_ 27.8 Hz and from Eq. 15.1 d v 0.280m 27.8Hz 7.78 ms e x direction. 15.7 a f v X 8.00 m s 0.320 m 25.0 Hz T f 1 25.0Hz 4.00 x 10 2 s k 2n X 2n 0.320 m 19.6 rad m. b y x t 0.0700 m cos 2nI t 25.0 Hz -X-- 0.320 m c 0.0700 m cos 2n 0.150 s 25.0Hz 0.360 m 0.320 m -4.95 cm. d The argument in the square brackets in the expression used in part c is 2n 4.875 and the displacement will next be zero when the argument is 10n the time is then T 5 - x X 1 25.0 Hz 5 - 0.360 m 0.320m 0.1550 s and the elapsed time is 0.0050 s e T 2 0.02 s. 15.8 a b 15.9 a -Ak sin kx mt dx d2 y dx2 -Ak2 cos kx mt dy À d2y 2 . . -Am sin kx mt y -Am cos kx mt dt dt2 1 d y L-2 d y __i _. _ _ -i . r t i _ and so kr andy x t is a solution of Eq. 15.12 with v m k. dx m dt dy d y 2 b Ak cos kx mt y -Ak sin kx mt dy . . .x d2y 2 . .x -d Am cos kx mt - y - Am sm kr mt and so and y x t is a solution of Eq. 15.12 with v rn k. c Both waves are moving in the - x -direction as explained in the discussion preceding Eq. 15.8 . d Taking derivatives yields vy x t -mA cos kx mt and .
