Waves

JEE Main level, single correct, medium

103 of 142

Question 103 of 142

5 beats/ second are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m0.95 \mathrm{~m} or 1 m1 \mathrm{~m}. The frequency of the fork will be:

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Answer: (A) 195 Hz195 \mathrm{~Hz}

Probable frequencies of tuning fork be n±n \pm 5
Frequency of sonometer wire, n∝1ln \propto \frac{1}{l}
∴n+5n−5=10095⇒95(n+5)=100(n−5) or, 95n+475=100n−500 or, 5n=975 or, n=9755=195 Hz\begin{aligned} &\therefore \frac{n+5}{n-5}=\frac{100}{95} \Rightarrow 95(n+5)=100(n-5) \\ &\text { or, } 95 n+475=100 n-500 \\ &\text { or, } 5 n=975 \\ &\text { or, } n=\frac{975}{5}=195 \mathrm{~Hz} \end{aligned}

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