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

Explanation

At nodes amplitude of wave is zero.
`4 sin [(pi x)/(15)]=0 or (pi x)/(15) = 0,pi,2pi,3pi, ………`
So ` x= 0, 15,30, 45, 60 cm`
[as length of string = 60 cm].