(i) For the wave on the string described in the question, we have seen that, L = 1.5 m and λ = 3 m. It is clear that L = λ/2 and for a string clamped at both ends, it is possible only if both the ends behave as nodes and there is one anti-node in between.

a) Yes, all the string particles except the nodes, vibrate with the same frequency, v = 60 Hz.

b) As all string particles lie in one segment, all of them are in same phase.

c) Amplitude varies from particle to particle, at anti-nodes amplitude is 2a i.e. 0.06 m. It gradually falls towards nodes. At the nodes the amplitude is zero.

(ii) Distance from one end, x = 0.375 m

Amplitude at the distance of 0.375 is given by,

A = 0.042 m