A stretched string is rigidly fixed at both ends and is set into transverse vibration.
(i) Define a node and an antinode for a standing wave on the string.
(ii) Explain, with reasoning based on boundary conditions, why the string can vibrate only at certain discrete frequencies and not at all possible frequencies.
(iii) Draw neatly the first three normal modes of vibration for the string and clearly mark the positions of nodes and antinodes in each mode.