Question

A chord attached about an end to a vibrating fork divides it into $6$ loops, when its tension is $36\text{N}$. The tension at which it will vibrate in $4$ loops is
(correct answer + 1, wrong answer - 0.25)

• A. $24\text{N}$
• B. $36\text{N}$
• C. $64\text{N}$
• D. $81\text{N}$

Answer 1

The correct option is D $81\text{N}$

For waves along a string :
$v\propto \sqrt{T}$
$\Rightarrow \lambda \propto \sqrt{T}$
Now, for $6$ loops: $3{\lambda }_1=L\Rightarrow {\lambda }_1=L/3$
and for $4$ loops $2{\lambda }_2=L\Rightarrow {\lambda }_2=L/2$
$\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}=\frac{2}{3}$
$\Rightarrow T_2=\frac{9}{4}\times T_1=\frac{9}{4}\times 36$
$=81\text{N}$