The vibrations of a string of length `60cm` fixed at both ends are represented by the equation----------------------------
`y = 4 sin ((pix)/(15)) cos (96 pit)`
Where `x` and `y` are in `cm` and `t` in seconds.
(i) What is the maximum displacement of a point at `x = 5cm`?
(ii) Where are the nodes located along the string?
(iii) What is the velocity of the particle at `x = 7.5 cm` at `t = 0.25 sec`.?
(iv) Write down the equations of the component waves whose superpositions gives the above wave.

Explanation

One comparing the given equation with equation, we get
`y = "A sin kx cos" omega t `
`y = 2 [ sin ((pi x)/(15) + 96 pi t ) + sin ((pix)/(15) - 96 pi t )]`
Thus the waves are of the same amplitude and frequency, but travelling in opposite direction which thus, superimpose to give a standing wave,
The equations of component waves are
`y_(1) 2 sin ((pi x)/(15)+ 96 pi t )`
and ` y_(2) = 2 sin ((pi x)/(15) + 96 pi t )`