[المتفيزق]

yes my dear;
this is a travelling sine wave so we may suggest the solution as:
y(x,t) = A sin (kx - wt) in the +ve x direction.
now, the highest point is 4 mm so that : A = 0.004m
also the periodic time is 0.04 sec which is the time taken for complete period.
this means that w = 2pi/0.04 rad/sec ( nearly 160 rad/sec)
to evaluate k we have:
y(x=0.09,t=0) = 0.003m so we substitute to have:
0.03 = 0.04 sin(0.09k - 0) which implies:
sin(0.09k) = 0.75 I think this angle is nearly pi/4 or nearly 0.8 so that:
k = 0.8/0.09 = 9 m-1
thus the velocity is : w/k = 160/9 = 16m/sec approximately...


let's check in hurry...
take t= 0.05 sec at the profile of x=0 we have:
y(0,0.005) = 0.004 sin(0 - 160 . 0.05) = - 0.004 . sin(8)m
evaluate sin (8) radial ( i think it is nearly -0.99) so that we have:
y = 0.004 . 0.99 = 0.004 m (approx.)



another evidence: take y(x=0.09, t=0.005) which is zero in the graph...lets see>>>
y(0.09,0.005) = 0.004 sin[9 (0.09) - 160 (0.005)] = 0.004 sin(0.81 -0.8) = 0 !!!
thus , our soln. is ok...

the question says what if the motion is along ( -ve direction) not +ve that is of me...
the soln. is the same , but you change the -wt to +wt and continue soln.
thanks