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

Options

A. 4
B. 16
C. 5
D. 15

Answer

B

Explanation

Let the string vibrates in p loops, wavelength of the pth mode of vibration of given by
`lamda_p=(2l)/p`
Given `y=2 sin ((4 pi x)/15) cos (96 pi t)`
or `y=2[sin((4pix)/15+95pix)+sin((4pix)/15-96pit)`
`v= (96 pi)/(2 pi)=48 Hz and k=(4 pi)/15`
`1/48=(2 times60)/p times (4pi)/(15 times96pi)`
`impliesp=16`