The vibrations of a string of length 60 cm fixed at both the ends are represented by the equation `y=2 sin ((4pi x)/(15)) cos (96pit)`, where `x and y` are in cm. The maximum number of loops that can be formed in it, is

Options

A. 6
B. 16
C. 5
D. 15

Answer

B

Explanation

Given, `y=2 sin ((4pi x)/( 15)) cos (96pi t) and I= 60 "cm"`
We know that `f = (P)/(2I) xx v`
where, `P = ` number of loops
`(96 pi)/( 2pi) = (P)/( 2 xx 60) xx (omega )/( K)`
`(96pi)/( 2pi ) = (P)/( 2 xx 60) xx (96pi)/( (4pi)/(15) ) rArr P = 16`