The string fixed at both ends has standing wave nodes for which distance between adjacent nodes is `x_1`. The same string has another standing wave nodes for which distance between adjacent nodes is `x_2`. If `l` is the length of the string then `x_2//x_1=l(l+2x_1)`. What is the difference in numbers of the loops in the two cases?

Options

A. `1`
B. `2`
C. `3`
D. `4`

Answer

B

Explanation

Let no. of loops formed in first case `=n`
`x_1n=l` .(i)
Let no. of loops formed in second case `=(n+k)`
`x_2(n+k)l` .(ii)
From (i) and (ii) `x_2[(l)/(x_1)+k]=l,(x_2)/(x_1)=(l)/(l+kx_1)`
Comparing with `(x_2)/(x_1)=(l)/(l+2x_1),k=2`