Question

A sonometer wire under tension $T$ is in unison with a tuning fork of frequency $250$ Hz. If now the sonometer wire is replaced by another wire of the same diameter but low density, the number of loops shall-

• A. Decrease
• B. Increase
• C. Remain the same
• D. Incomplete information

Answer 1

The correct option is A Decrease

velocity of wave:( Let $p$ be number of loops)
$v=\frac{p}{2l}\sqrt{\frac{F}{\mu }}$
$v=\frac{p}{2l}\sqrt{\frac{F}{\pi r^2\rho }}$
$p=v\left(2l\right)\frac{\sqrt{\pi r^2\rho }}{\sqrt{F}}p\propto \sqrt{\rho }$
As density of new wire is less than that of sonometer wire, so number of loops shall decrease.