Question

Two strings of the same material and the same area of cross-section are used in Sonometer experiment. One is loaded with $12kg$ and the other with $3kg$. The fundamental frequency of the first string is equal to the first overtone of the second string. If the length of the second string is $100cm$, then the length of the first string is :

• A. $300cm$
• B. $200cm$
• C. $100cm$
• D. $50cm$

Answer 1

The correct option is C $100cm$

fundamental frequency $f=\frac{1}{2l_1}\sqrt{\frac{T_1}{\mu }}$
first over tone $f^{{}^{\prime }}=\frac{2}{2l_2}\sqrt{\frac{T_2}{\mu }}$
given $f=\frac{1}{2l}\sqrt{\frac{12}{\mu }}=\frac{2}{2l_1}\sqrt{\frac{3}{\mu }}$
$f^{{}^{\prime }}=\frac{2}{2l_2}\sqrt{\frac{3}{\mu }}$
$\therefore f^{{}^{\prime }}=f\Rightarrow l_1=l_2=100cm$