The vibrations of a string of length 60 cm fixed at both ends are represented by the equation `y=4sin((pix)/15) cos (96 pi t)`, where x and y are in cm and t in seconds.
(a)What is the maximum displacement of a point at `x = 5cm`?
(b)Where are the nodes located along the string?
(c)What is the velocity of the particle at x=7.5cm and t=0.25s?
(d)Write down the equations of the component waves whose superposition gives the above wave.

Explanation

As `y = 4 sin (pi x //15) cos (96 pi t)`
`(dy)/(dt) = - 4 sin[(pix)/(15)] sin (96 pi t) xx (96pi)`
So the velocity ofthe particle at x = 7.5 cm and t = 0.25 s
`v_(pa) = -384 pi sin(7.5 pi//15) sin (96 pixx 0.25)`
`v_(pa) =-384 pi xx 1xx 0 =0`