Question

A chord attached about an end to a vibrating fork divides it into 6 loops, when its tension is 36 N. The tension at which it will vibrate in 4 loops is :

Answer 1

For waves along a string: $V\propto \sqrt{T}$

$\because v\propto \lambda$
$\Rightarrow \lambda \propto \sqrt{T}$
Now, for 6 loops $3{\lambda }_1=L\Rightarrow {\lambda }_1=\frac{L}{3}$

and for 4 loops :$2{\lambda }_2=L\Rightarrow {\lambda }_2=\frac{L}{2}$

$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{2}{3}$
$\Rightarrow \frac{T_2}{T_1}=\frac{9}{4}$

$\Rightarrow T^2=\frac{9}{4}\times T=\frac{9}{4}\times 36=81N$

Final answer:(d)