When tension ' $\mathrm{T}$ ' is applied to a sonometer wire of length ' $\mathrm{l}$ ' it vibrates with the…
When tension ' $\mathrm{T}$ ' is applied to a sonometer wire of length ' $\mathrm{l}$ ' it vibrates with the fundamental frequency ' $n$ '. Keeping the setup same, when the tension is increased by $8 \mathrm{~N}$, the fundamental frequency becomes three times the earlier. The initial tension applied to the wire was
$2 \mathrm{~N}$
$1 \mathrm{~N}$
$0.5 \mathrm{~N}$
$4 N$
Solution
The initial fundamental frequency of wire can be written as,
On dividing equation ( 2 ) by equation (1), we get
$\begin{aligned} & 3=\sqrt{\frac{T+8 N}{T}} \\ & \Rightarrow 9 T=T+8 N \\ & \Rightarrow T=1 N\end{aligned}$
On dividing equation ( 2 ) by equation (1), we get
$\begin{aligned} & 3=\sqrt{\frac{T+8 N}{T}} \\ & \Rightarrow 9 T=T+8 N \\ & \Rightarrow T=1 N\end{aligned}$