Question

Two strings A and B made of same material, have lengths $l_A$ and $l_B$ and are connected to two other comparitively denser medium strings having masses $M_A$ and $M_B$, the upper ends being supported by rigid supports. If $f_A$ and $f_B$ are their fundamental frequencies of their vibrations, then $f_A:f_B$ is

• A. $\frac{M_A{l}_A}{M_B{l}_B}$
• B. $\frac{l_A}{l_B}\sqrt{\frac{M_A}{M_B}}$
• C. $\frac{M_A}{M_B}\sqrt{\frac{l_A}{l_B}}$
• D. None of these

Answer 1

The correct option is D None of these


Both the strings will vibrate as if their both ends are fixed.
At equilibrium,
$T_A=M_{A}g$ and $T_B=M_{B}g$
Fundamental frequency.
$f=\frac{V}{2l}=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
$\Rightarrow \frac{f_A}{f_B}=\sqrt{\frac{T_A}{T_B}}\times \frac{l_B}{l_A}$
$\therefore f_A:f_B=\frac{l_B}{l_A}\sqrt{\frac{M_A}{M_B}}$
$\Rightarrow f_A:f_B=\frac{l_B}{l_A}\sqrt{\frac{M_A}{M_B}}$