What is the maximum speed of any point on the string?

Question

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz.

Answer 1

The equation of the point on the string is
f(t) = 2.*sin(100*2*pi*t)
where t is time in seconds.

The speed is f'(t), or
2*cos(100*2*pi*t)*100*2*pi

The maximum speed happens when cos(100*2*pi*t) is 1, which happens at many different times, but that doesn't matter as long as it happens at least at one time, which it does (t=0).

So the maximum speed is 400*pi cm/second