(i) Define a node and an antinode in the context of a stationary wave on a stretched string fixed at both ends.
(ii) Explain why a stretched string fixed at both ends can vibrate only at certain discrete frequencies and not at all possible frequencies.
(iii) Keeping the length of the string fixed, predict qualitatively how its fundamental frequency will be affected in each of the following cases, giving reasons in each case:
(a) the tension in the string is increased,
(b) the linear mass density of the string is decreased.