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.

Answer

(i) `y_(1) = 1.5 cos {(pi//20)x - 72pit}`,
`y_(2) = 1.5 cos {(pi//20)x + 72 pit)`
(ii) `10, 30, 50 cm` and `0 , 20 , 40 , 60 cm`
(iii) `0`