if a [b]sinusoidal wave[/b] is travelling along a string n take the moment when a [b]particle's displacement is max. [/b] then :

at the [b]top of the hump [/b] [b]tension[/b] would b [b]tangential[/b] (since the wave function is sin(t)) so the [b]net tension is zero[/b]....(tell me if i m wrong somewhere).(tension obeying [b]newtons third law [/b] ).

since the particle have max. displacement the [b]vel of the particle at that instsnt is zero [/b] also tension is zero at that position then [b]which force is responsible [/b] for providing that particle a [b]necessary acceleration[/b] so that it can get back 2 its original position.

if i take a string element d(s) not a particle den the resolving the tangential tension (which is not fully in horizontal direction) in vertical n horizontal directions , the tensions in horizontal (opposite direction)cancel each other n therefore the net is in the vertical direction n yes,satisfies the condition for S.H.M.....since that net force provides necessary acceleration for that string element considered.