One end of a string with a linear mass density of 3.22 x 10^-4kg/m is connected to an oscillator with a frequency of 54.6 Hz. The other end is connected to a hanging variable mass. The string passes over a pulley, and the string between the oscillator and the pulley can vibrate freely. The length of the vibrating section of the string is0.646 m. What mass must be attached so that the string vibrates with

(i) one antinode between the pulley and the oscillator?

(ii) three antinodes between the pulley and the oscillator?