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Neela Pillay
Asked: 2022-10-29T16:54:13+05:30 In:

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.

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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  1. 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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