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.

Options

A. `2 sqrt(3) cm`
B. `4 cm`
C. zero
D. `4 sqrt(2) cm`

Answer

A

Explanation

For ` x = 5 , y = 4 sin ((5 pi)/( 15)) cos (96 pi t)`
` = 2 sqrt(3) cos (96 pi t)`
So , `y` will be minimum when `cos (96 pi t ) = max = 1`
`y_(max) = 2 sqrt(3) "cm at" x = 5`