Answer the following with reference to standing waves on a stretched string fixed at both ends.
(a) Explain why nodes are always formed at the fixed ends when a stationary wave is established on the string.
(b) Describe qualitatively how the positions of nodes and antinodes would change, if at all, when the tension in the string is gradually increased while its length and mass per unit length remain constant.
(c) Successive harmonics of a string have frequencies in the ratio 1:2:3:… . Explain how this ratio arises from the geometry of the standing wave patterns.