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The harmonic wave yi = (2.0 xx 10^(-3)) ...

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.

Text Solution

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The correct Answer is:
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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