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The harmonic wave `y_i = (2.0 xx 10^(-3)) cos pi (2.0x - 50t)` travels along a string towards a boundary at x=0 with a second string. The wave speed on the second string is `50 m//s`. Write expressions for reflected and transmitted waves. Assume SI units. |
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Answer» Correct Answer - A::B::C Speed of wave in first medium is, `v_1` = (Coefficient of `t`)/(Coefficient of `x`) = `50/2 = 25 m//s ` `v_2 = 50m//s` `A_i = 2xx 10^(-3)m`. `A_r = ((v_2-v_1)/(v_2+v_1))A_i = 2/3 xx (10^-3)m ` ` A_t = ((2v_2)/(v_1 +v_2)) A_i = 8/3 xx (10^(-3))m ` . In second medium, speed becomes two times. Therefore, `lambda` also becomes two times. So, k remains one-half, value of `omega` will remain unchanged. Further, second medium is rarer medium `(v_2 gt v_1)`. Hence there is no change in phase angle anywhere. `:. y_r = 2/3 xx 10^(-3) cos pi (2.0x + 50t)` and `y_t = 8/3 xx 10^(-3) cos pi (2.0x + 50t)` . |
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