Question

The vibrations of a string of length 60 cm fixed at both the ends are represented by the equation $y=2\sin \left(\begin{array}{c}\frac{4\pi x}{15}\end{array}\right)\cos \left(96\pi t\right)$, where x and y are in cm. The maximum number of loops that can be formed in it is

• A. 6
• B. 16
• C. 5
• D. 15
• E. 8

Answer 1

Answer: (B)

16

Given

Y = 2 sin($4\pi x/15$) cos($96\pi t$) ........(1)

This equation represents the stationalry equation of the type
Y = 2a sin($2\pi x/\lambda$) cos($96\pi t$)........(2)

Compairing the equations we get,

$2\pi x/\lambda$ = $4\pi x/15$

$\lambda =7.5cm$

The string is of length 60 cm while the wavelenght is 7.5 cm, hence location of nodes are

$x=0,7.5/2,7.5,11.25,15,.....,60.$

hence maximum number of loops formed is $16$.