(i) For the wave on a string described in Exercise 15.11, do all the points on the string oscillate with the same (a) frequency, (b) phase, (c) amplitude? Explain your answers. (ii) What is the amplitude of a point 0.375 m away from one end?

(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