A stretched string 80 cm long is fixed at both ends. A point P on the string is 22 cm from the left end. The string is vibrating in a certain harmonic such that point P lies exactly midway between a node and the nearest antinode.
(i) Show that the harmonic number must be even for this condition to hold.
(ii) Determine the smallest harmonic number that satisfies the given condition for point P.
(iii) For this harmonic, calculate the distance of point P (a) from the nearest node and (b) from the left end of the string.