545_Physics ProblemsTechnical Physics

545_Physics ProblemsTechnical Physics - Chapter 18 2 and =...

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Chapter 18 547 P18.68 (a) With k = 2 π λ and ωπ == 2 2 f v : yx t A kx t A xv t , sin cos sin cos bg F H G I K J F H G I K J 22 ω (b) For the fundamental vibration, 1 2 = L so yxt A x L vt L 1 2 ,s i n c o s = F H G I K J F H G I K J ππ (c) For the second harmonic 2 = L and A x L vt L 2 2 i n c o s = F H G I K J F H G I K J (d) In general, n L n = 2 and A nx L nv t L n i n c o s = F H G I K J F H G I K J 2 P18.69 (a) Let θ represent the angle each slanted rope makes with the vertical. In the diagram, observe that: sin . 100 2 3 m 1.50 m or 41 8 .. Considering the mass, F y = 0: 2 Tm g cos = or T = ° = 12 0 9 80 24 1 8 78 9 cos . . kg m s N 2 ej FIG. P18.69 (b) The speed of transverse waves in the string is v T = µ 78 9 281 . N 0.001 00 kg m ms For the standing wave pattern shown (3 loops), d = 3 2 or 2200 3 133 . . m m af Thus, the required frequency is
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