A string of length 1.2m is fixed at both ends and vibrates in its fourth harmonic. The speed of transverse waves on the string is 180ms−1.
(i) How many nodes and how many antinodes are present on the string in this mode?
(ii) Calculate the distance between two consecutive nodes.
(iii) A paper rider is placed at a point 0.15m from one end of the string. Will it remain at rest or be thrown off during vibration? Justify your answer.
(iv) If the maximum displacement of a particle at an antinode is 4mm, write the mathematical expression for the displacement of the particle situated 0.15m from an end and state the value of its maximum speed.