A string of length is fixed at both ends. It is vibrating in its 3^ rd overtone with maximum amplitude'a'. The amplitude at a distance / 3 from one end is

Step-by-step solution

For a string vibrating in its n ^ th overtone ( n +1)^ th harmonic) y =2 ~A ( ( n +1) x L ) t array l For .x= 3 ] 2 A=a & n=3 y= [a ( 4 3 ) ] t =a 4 3 t=-a ( 3 2 ) t array i.e. at x= 3 , the amplitude is 3 a 2