hw1_sol - PHY 102 Homework#1 Solution 1 From the formula =...

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PHY 102: Homework #1 Solution 1. From the formula f v v.T λ = = , one obtain : (a) For 0.1m λ = , 340m/s v s = : 340Hz 1.0m 340m/s f = = . (b) For the electromagnetic wave m/s 10 3 C v 8 s × = = , therefore Hz 10 3 f 8 × = 2. The wave length interval is m to m 7 7 10 7 10 4 - - × × . From the same formula as in the above, one found : - Hz m s m 15 7 8 10 75 . 0 10 4 / 10 3 λ × = × × = - - Hz m s m 15 7 8 10 42 . 0 10 7 / 10 3 λ × = × × = - Thus the frequencies of the electromagnetic waves are Hz 15 10 42 . 0 × to Hz 15 10 75 . 0 × 3. The wave string equation being ( ( kx ω t sin 4.00 t x, y - × = , With rad/sec 10 6.0 2 × = ϖ and rad/m 6.0 k = (a) The amplitude : A=4.0mm (b) The wavelength : m 1.04 6.0rad/m 3.14rad 2 k 2 π λ = × = = (c) The period : s 10 1.04 rad/s 10 6.0 3.14rad 2 2 π T 2 2 - × = × × = = ϖ (d) Wave speed : m/s 100 s 10 1.04 1.04m T λ v 2 = × = = - (e) The wave is traveling in the positive direction of x. 4. This is a Bonus question. Clever students should not hesitate to attack this problem. y y y y y
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One must show that y , the distance between two adjacent fringes, are equals. Recall that: d λ L m y m = y is given by m m m y y y - = + 1 One has, = - = 1 2 1 y y y d λ L d λ L 1) - 2 ( d λ L - d λ L 2 = = = - = 2 3 2 y y y d λ L d λ L 2) - 3 ( d λ
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