wavy waves

consider a plane progressive wave y=A sin(kx-wt) propagating in a string having tension F.

What is the linear impulse given by the F-transverse acting at x=0 on the time interval t=0 to t= T/4?
(asumptions tanθ≈sinθ; Amplitude A is small so tension can be assumed constant throughout the string)

i) \frac{\mu A\omega }{2k}
ii)\frac{\mu A\omega }{k}
iii)\frac{2\mu A\omega }{k}
iv) none of these