(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

All the points on the string have same frquency except at the nodes. (where frequency is zero).
But the amplitude of vibration is different at different points.
Amplitude of vibration is given by
`y(x, t) = 0.06 sin ((2pi)/(3) x)`
At x = 0.375 m
`y(x, t) = 0.06 sin ((2pi)/(3) xx 0.375)`
`= 0.06 sin (0.25 pi)`
`= 0.06 "sin" (pi)/(4)`
`= (0.06)/(sqrt(2)) = 0.042` m