Question 62 of 142

A sonometer wire of resonating length $90 \mathrm{~cm}$ has a fundamental frequency of $400 \mathrm{~Hz}$ when kept under some tension. The resonating length of the wire with fundamental frequency of $600 \mathrm{~Hz}$ under same tension _____$\mathrm{cm}$.

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Answer: 60

$\begin{aligned} & \mathrm{f}_0=400 \mathrm{~Hz} ; \mathrm{v}=\sqrt{\frac{\mathrm{T}}{\mu}}=\text { constant } \\ & \frac{\lambda}{2}=\mathrm{L} ; \quad \mathrm{v}=\mathrm{f}_0 \lambda\end{aligned}$
$\begin{aligned} & \frac{\mathrm{v}}{2 \mathrm{f}_0}=\mathrm{L} \Rightarrow \mathrm{v}=2 \mathrm{Lf}_0 \\ & \mathrm{~L}^{\prime}=\frac{\mathrm{v}}{2 \mathrm{f}^{\prime}}=\frac{2 \mathrm{Lf}_0}{2 \mathrm{f}^{\prime}} \\ & =\frac{\mathrm{Lf}_0}{\mathrm{f}^{\prime}}=\frac{90 \times 400}{600}=60\end{aligned}$