Question

A string of length l is fixed at both ends it is vibrating in its 3rd overtone

Answer 1

As, it is shaking in its third overtone then nodes will be attained at  :

x=0 ,l / 4, 2l / 4, 3l / 4,l

1st equation of motion is y = a sin(√4x / l)cos wt  

By putting x = l / 3  

amplitude =a sin(√4l / 3l) =a sin(√4/ 3) = a(√3 / 2)