In a standing wave experiment , a `1.2 - kg` horizontal rope is fixed in place at its two ends `( x = 0 and x = 2.0 m)` and made to oscillate up and down in the fundamental mode , at frequency of `5.0 Hz`. At `t = 0` , the point at `x = 1.0 m` has zero displacement and is moving upward in the positive direction of `y - axis` with a transverse velocity `3.14 m//s`. Speed of the participating travelling wave on the rope isA. `6 m//s`B. `15 m//s`C. `20 m//s`D. `24 m//s`

In a standing wave experiment , a `1.2 - kg` horizontal rope is fixed

1.	In a standing wave experiment , a `1.2 - kg` horizontal rope is fixed in place at its two ends `( x = 0 and x = 2.0 m)` and made to oscillate up and down in the fundamental mode , at frequency of `5.0 Hz`. At `t = 0` , the point at `x = 1.0 m` has zero displacement and is moving upward in the positive direction of `y - axis` with a transverse velocity `3.14 m//s`. Speed of the participating travelling wave on the rope isA. `6 m//s`B. `15 m//s`C. `20 m//s`D. `24 m//s`
Answer» Correct Answer - C `mu = (1.2)/(2) = 0.6 kg//m` `n = 5 Hz` `lambda = 2 l = 4 m` `V = n lambda = 5 xx 4 = 20 m//s` Using `v = sqrt((T)/(mu))` `T = 20^(2) xx 0.6 = 240 N` `((delta y)/( delta t))_(max) = 3.14 m//s` `( 2 A)omega = 3.14` Amplitude `2A = (3.14)/(2 xx (3.14) xx 5) = 0.1 m` Equation of standing wave is `y = (0.1) sin (pi)/(2) s sin (10 pi) t`

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