Question

A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension _______ cm.

Answer 1

Correct answer is : 60

\(\mathrm{f}_{0}=400 \mathrm{~Hz}\ ; \mathrm\ {v}=\sqrt{\frac{\mathrm{T}}{\mu}}=\) constant

\(\frac{\lambda}{2}=\mathrm{L} \ ; \quad \mathrm{v}=\mathrm{f}_{0} \lambda\)

\(\frac{\mathrm{v}}{2 \mathrm{f}_{0}}=\mathrm{L} \Rightarrow \mathrm{v}=2 \mathrm{Lf}_{0}\)

\(\mathrm{L}^{\prime}=\frac{\mathrm{v}}{2 \mathrm{f}^{\prime}}=\frac{2 \mathrm{Lf}_{0}}{2 \mathrm{f}^{\prime}}\)

\(=\frac{\mathrm{Lf}_{0}}{\mathrm{f}^{\prime}}=\frac{90 \times 400}{600}=60\)