JEE Mains · Physics · STD 11 - 14. waves and sound
A tuning fork resonates with a sonometer wire of length \(1 \mathrm{~m}\) stretched with a tension of \(6 \mathrm{~N}\). When the tension in the wire is changed to \(54 \mathrm{~N}\), the same tuning fork produces \(12\) beats per second with it. The frequency of the tuning fork is _______ \(\mathrm{Hz}\).
- A \(4\)
- B \(5\)
- C \(6\)
- D \(7\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
\(\mathrm{f}=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}\) \(\mathrm{f}_1=\frac{1}{2} \sqrt{\frac{6}{\mu}} \mathrm{f}_2=\frac{1}{2} \sqrt{\frac{54}{\mu}}\) \(\frac{\mathrm{f}_1}{\mathrm{f}_2}=\frac{1}{3} \mathrm{f}_2-\mathrm{f}_1=12\) \(\mathrm{f}_1=6 \mathrm{HZ}\)
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