(i) The transverse displacement of a string (clamped at its two ends ) is given by `y(x,t)=0.06 sin[ (2pi)/(3)x] cos 120pit,`
where x, y are in m and t is in s.
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 `0.375m` away from one end?

Explanation

(i) ,(a) Yes, except at the nodes
(b) Yes, except at the nodes
(c) No
(ii) 0.042 m
(ii) 0.042 m
Explanation:
(i)
(a) All the points on the string oscillate with the same frequency, except at the nodes which have zero frequency.
(b) All the points in any vibrating loop have the same phase, except at the nodes.
(c) All the points in any vibrating loop have different amplitudes of vibration.
(ii) The given equation is:
`y(x,t)=0.06 "sin"((2pi)/(3)x)"cos"(120 pit)`
For x= 0.375 m and t=0
Amplitude=Displacement `=0.06 "sin"((2pi)/(3)x)"cos"0`
`=0.06 "sin"((2pi)/(3)xx0.375)xx1`
`=0.06 "sin"(0.05 pi)=0.06 ((pi)/(4))`
`=0.06xx(1)/(sqrt(2))=0.042 m`