Question

You are given two waves, a transverse wave that moves to the right f1(x) and a transverse wave that moves to the left f2(x), on a string. As the problem begins, the wave f1(x) is moving to the right at v1 = +1 m/s and the wave f2(x) is moving to the left at v2 = -1m/s. what is the shape of the wave after 3s?

Answer 1

It will depend upon the amplitudes and phases of the two waves. You need to provide more information.

You need to write equations
Amplitude = f(x,t)
for the two waves, and add them

If the amplitudes are equal, you get a standing wave with nodes every half-wavelength