the figure below shows the displacement y versus time t of thepoint on a string

Question

the figure below shows the displacement y versus time t of thepoint on a string at x = 0, as a wave passes through that point.The scale of the y axis is set by ys = 6.0mm. The wavehas form y(x, t) = ym sin(kx - t+ ). What is ? (Caution: A calculator does not always give the proper inversetrig function, so check your answer by substituting it and anassumed value of into y(x, t) and then plotting thefunction.) *sorry about the diagram!! *

Explanation / Answer

    for the given problem first we set     x = 0 in     y = ym sin (k x - t + )which gives us     y = ym sin(- t + )     as the function being plotted in the graph     we note that it has a positive slope at t =0     dy / dt = d ym sin(- t +) / dt               = - ym cos(- t + ) > 0 at t =0     this implies that - cos() > 0 andconsequently that is in either the second or thirdquadrant     the graph shows in the text at t = 0 y = 2.00mm     and at some time t     ym = 6.00 mm     y = ym sin(- t +)|t = 0     = sin-1(1 / 3)        = 0.34 rad or 2.8rad

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