有關波動學的問題(知答案,但不明白何解) 20點

The equation y=6.0sin(0.020x+4.0t ) gives the variation of y as a function of x (distance) and t (time).
The question asks to find the maximum velocity of vibration of a particle on the string.
Since each particle along the string behaves in a similar way, we can just take any one of the particles. The simplest way is to select the particle at x=0. But you can, if you wish, select a particle at any distance x from the origin.
For example, if you select a particle at distance x1, say, then the equation describing the vibrational motion of this particular particle is:
y = A.sin(k.x1+wt)
since velocity v = dy/dt (velocity = rate of change of displacement)
we have, v = d[A.sin(k.x1+wt )]/dt
i.e. v = A.wcos(wt), since (k.x1) is a constant
The values of the cosine function varies between -1 to +1, that is, when it has a max value of +1 , this would give a max value to v
therefore, v(max) = A.w