Waves

JEE Main level, single correct, medium

78 of 142

Question 78 of 142

A string is stretched between fixed points separated by 75 cm75 \mathrm{~cm}. It is observed to have resonant frequencies of 420 Hz420 \mathrm{~Hz} and 315 Hz315 \mathrm{~Hz}. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is

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Answer: (B) 105 Hz105 \mathrm{~Hz}

n2ℓ(v)=315,(n+1)2ℓv=420\frac{\mathrm{n}}{2 \ell}(\mathrm{v})=315, \frac{(\mathrm{n}+1)}{2 \ell} \mathrm{v}=420
Solving
v2ℓ=105\frac{\mathrm{v}}{2 \ell}=105

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