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A string is stretched between fixed points 75 cm apart. It has resonant frequencies of 420 Hz and 315 Hz, with no other resonance between them. The lowest resonant frequency of this string is

Asked in JEE Main 2006 · Nodes, antinodes and harmonics

Answer: (2) 105 Hz

Step-by-step solution

For a string fixed at both ends the resonances are nf₁, and consecutive ones differ by f₁.

f₁=420-315=105 Hz, consistent with 315=3f₁ and 420=4f₁.

Why the other options are wrong

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