Question

A uniform string of fundamental frequency of vibration $f$ is divided into two segments by means of a bridge. If $f_{1}$ and $f_{2}$ are fundamental frequencies of these segments then

• A. $f_{1} f_{2}=f\left(f_{1}+f_{2}\right]$
• B. $2 f=f_{1}+f_{2}$
• C. $\sqrt{f}=\sqrt{f_{1}}+\sqrt{f_{2}}$
• D. $\sqrt{f_{1} f_{2}}=2 f$

Answer 1

Answer: (A)

$I=I_{1}+I_{2} $
$f_{1}=\frac{v}{2 l_{1}}$
or $l_{1}=\frac{v}{2 f_{1}}$
Similarly,
$l_{2}=\frac{v}{2 f_{2}} $
$l=\frac{v}{2 f} $
$\frac{v}{2 f}=\frac{v}{2 f_{1}}+\frac{v}{2 f_{2}} $
$\frac{1}{f}=\frac{1}{f_{1}}+\frac{1}{f_{2}}$
$f=\frac{f_{1} f_{2}}{f_{1}+f_{2}} $
$f\left(f_{1}+f_{2}\right]=f_{1} f_{2}$