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Lesson_5.3_Homework_Solution

Lesson_5.3_Homework_Solution - Lesson 5.3 Homework...

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Lesson 5.3 Homework Solutions 1. (i) This wave pulse advances to the right with a speed of 5 ms -1 . Its velocity is 5 i . (ii) 0.07 m 5.0 m The figure shows how the pulse advances with time. The distance between successive maxima is 5 m indicating that the wave is moving to the right at 5 ms -1 . (iii) The maximum displacement occurs when the term x – 5t = 0. The maximum displacement = 0.07 m and this is the amplitude of the wave pulse. (iv) The wave pulses are the same as before, but they are advancing to the left with a speed of 5 ms -1 . Its velocity is -5 i . 2. f = 5 Hz, v = 10 m.s -1 , λ = v/f = 10/5 = 2.0 m, A = 0.1 m 1 2 2 2 k m π π π λ - = = = , ϖ = 2 π f = 10 π y(x,t) = A sin(kx – ϖ t) = A sin {k(x – vt)} y(x,t) = 0.1 sin ( π x – 10 π t) = 0.1 sin { π (x – 10t)} 3. (i) 0.3 m (ii) k = 12.57 m -1 .
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(iii) 2 2 12.57 0.5 m k π π λ = = = (iv) Angular frequency ϖ = 251 Hz (v) 251 1 1 , 40 0.025 2 2 40 H f T f z s ϖ π π = = = = = = (vi) 1 251 12. 2 57 0 v m s k ϖ - = = = (vii) y(3.0 m, 2.0 s) = 0.3 sin(12.57 × 3 – 251 × 2) = 0.3 sin(-465) = -0.013 m 4. (i) y(x,t) = 0.45 sin[3(x – 2t) + 1.2] = 0.45 sin(3x – 6t + 1.2) (ii) (iii) y(x,t) = 0.45 sin[3(x +2t) + 1.2] = 0.45 sin(3x + 6t + 1.2) 5.
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m 1 ax 1 1.12 13.4 0.07 15 0.48 0.48
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