Fundamental frequency of a sonometer wire is n. If
the length and diameter of the wire are doubled
keeping the tension same, then the new fundamental
frequency is

Options

A. `2n/sqrt(2)`
B. `n/(2sqrt(2))`
C. `sqrt(2)n`
D. `n/4`

Answer

b

Explanation

If the length of the wire between the two bridges is l,
then the frequecy of vibration is
`n=1/(2l)sqrt(T/m)=1/(2l)sqrt(T/(pir^(2)d))`
If the length and diameter `(="radius"/2)` of the wire are
doubled keeping the tension same, then new fundamental
frequency will be `n/4`.