Question

Two stratched strings of same material are vibrating
under some tension in fundamental mode. The ratio
of their froquencies is ` 1 : 2` and ratio of the length of
the vibrating segments is ` 1: 4` Then, the ratio of the
radii of the strings is
A. `2 : 1`
B. `4 : 1`
C. ` 3 : 2`
D. `8 : 1`

Answer 1

Correct Answer - d
`n=1/(2l)sqrt(T/(pir^(2)d))`
where, l is length, T is tension, r is radius and d is density.
Given, `n_(1)/n_(2)=1/2,l_(1)/l_(2)=1/4`
`therefore n_(1)/n_(2)=l_(2)/l_(1) sqrt(r_(2)^(2)/r_(1)^(2))rArr n_(1)/n_(2)=(l_(2)r_(2))/(l_(2)r_(1))`
`rArr therefore r_(1)/r_(2)=(n_(2)l_(2))/(n_(1)l_(1))=2xx4 = 8 : 1`