wave- displacement for a point

1. The problem statement, all variables and given/known data



A wave on a string has a wave function with the form of:

y(x,t)=0.02sin(6.35x+2.63t)



Find the shortest time for the displacement of the string at any point on the chain changes from 0.01m to -0.02m.



3. The attempt at a solution



The answer said we can set x=0.

And 0.01=0.02sin(2.63t1), 3*3.14/2=2.63t2, where t1 is initial time and t2 is final time.

then t1=0.2s and t2=1.6s, so t2-t1=1.4s



But I don't understand where 3*3.14/2=2.63t2 comes from.

And when I tried to follow the answer and calculate, the calculated answers don't seem to be correct....



So how should I solve it?

Thank you very much.