String B has twice the length , twice the diameter twice the tension and twice the density of string A. Then the overtone of B that will be in unison will A is

Options

A. `1^(st)`
B. `3^(rd)`
C. `2^(nd)`
D. `4^(th)`

Answer

B

Explanation

`n_2/n_1 = l_1/l_2 xxd_1/d_2 xx(T_2xxe_1)/(T_1xxe_2) = 1/2 xx1/2 xx1 = 1/4`
`n_1 = (n_1)/(4) " Now , " P^(th) " overtone " = (P+1)^(th)` harmonic.
`therefore 3^(rd)` overtone = `4^(th)` harmonic